Free NEET Physics multiple-choice questions on Biot-Savart & Ampere's Law. Attempt each question and reveal the answer with a full explanation.
A long solenoid of length 50 cm, having 100 turns, carries a current of 2.5 A. The magnetic field at the centre of the solenoid is: 6.28 × 10 -4 T 3.14 × 10 -4 T 6.28 × 10 -5 T 9.42 × 10 -4 T A cylindrical conductor of radius R is carrying a constant current. The plot of the magnitude of the magnetic field B with the distance d from the centre of the conductor is correctly represented by the figure: Linear increase up to R and then hyperbolic decrease Constant up to R and then hyperbolic decrease Hyperbolic decrease from the centre Parabolic increase up to R and then linear decrease A bar magnet of length l and magnetic dipole moment M is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be M 3 M 2 M M 2 A uniform conducting wire of length 12a and resistance 'R' is wound up as a current carrying coil in the shape of, (i) an equilateral triangle of side 'a'. (ii) a square of side 'a'. The magnetic dipole moments of the coil in each case respectively are 3Ia 2 and Ia 2 3Ia 2 and 4Ia 2 4Ia 2 and 3Ia 2 3 ,Ia 2 and 3Ia 2 In a uniform magnetic field of 0.049 T , a magnetic needle performs 20 complete oscillations in 5 seconds as shown. The moment of inertia of the needle is 9.8 10 -6 kg m 2 . If the magnitude of magnetic moment of the needle is x 10 -5 Am 2 , then the value of ‘ x ’ is : 5 2 128 2 50 2 1280 2 An iron bar of length L has magnetic moment M . It is bent at the middle of its length such that the two arms make an angle 60 with each other. The magnetic moment of this new magnet is : M M/2 2M M/ 3 Given below are two statements : Statement I : Ferromagnetism is considered as an extreme form of paramagnetism. Statement II : The number of unpaired electrons in a Cr 2+ ion (Z = 24) is the same as that of a Nd 3+ ion (Z = 60). In the light of the above statements, choose the correct answer from the options given below : Statement I is false but Statement II is true Both Statement I and Statement II are true Both Statement I and Statement II are false Statement I is true but Statement II is false Two thin, long, parallel wires, separated by a distance d , carry current i in opposite directions. The magnetic field at a point exactly midway between them is: 0 i / π d 0 i / 2π d Zero 2 0 i / π d A square loop of side l carries a current i . The magnetic field at the center of the loop is: 2√2 0 i / π l √2 0 i / π l 0 i / 2π l 4 0 i / π l Two parallel long wires carry currents i 1 and i 2 with i 1 > i 2 . When the currents are in the same direction, the magnetic field at a point midway between the wires is 10 T. If the direction of i 2 is reversed, the field becomes 30 T. The ratio i 1/i 2 is: 2 3 1 4 Two wires of same length are shaped into a square of side 'a' and a circle of radius 'r'. If they carry the same current, the ratio of their magnetic moments is: /4 4/ /2 1 The magnetic field at the center of a circular current-carrying loop of radius R is B c . At what distance x from the center on the axis is the field B c/8 ? 3 R 2 R 3R 2R When a current-carrying loop is placed in a uniform magnetic field, the net force acting on it is: Always zero Zero only if it is a circular loop Zero only if it is a square loop Never zero The magnetic field at the centre of a circular loop of area A is B . The magnetic moment of the loop is: 2BA A 0 BA A 0 2BA 0 BA 2 0 A square loop of side l carries a current i . The magnetic field at the center of the loop is B . If the same current i is passed through a circular loop of the same perimeter as the square, the magnetic field at the center of the circular loop is B' . The ratio B/B' is: 8 2 / 2 8/ 2 2/8 2 2/8 The magnetic field at the center of a current-carrying circular coil of area A is B . The magnetic moment of the coil is: 2BA 3/2 0 BA 3/2 0 2 BA 3/2 0 0 A 3/2 2 B A circular loop of radius 0.3 cm carries a current of 2 A. The magnetic field at a distance of 4 cm from the center of the loop on its axis is approximately: 1.4 10 -8 T 2.8 10 -8 T 7.0 10 -7 T 3.5 10 -7 T A wire of length L is bent into a regular hexagon and a current I is passed through it. The magnetic field at the center of the hexagon is: 0 I L 6 3 0 I L 2 3 0 I L 3 0 I L 12 3 The magnetic field at the center of an equilateral triangular loop of side a carrying a current I is: 18 0 I / (4 a) 9 0 I / (4 a) 6 0 I / (4 a) 3 0 I / (4 a) A square loop of side a and a circular loop of radius r have the same perimeter. If they carry the same current I , the ratio of the magnetic field at the center of the square loop to that at the center of the circular loop is: 8 2 / 2 2 / 4 / 2 2 / 8 2 A current element I l is at the origin. What is the magnetic field at a point P(0, y, 0) if l = x i ? 0 4 I x y 2 k 0 4 I x y 2 j 0 4 I x y 3 k Zero A current loop consists of two identical semicircular parts each of radius R , one lying in the xy -plane and the other in the xz -plane. If the current in the loop is i , the resultant magnetic field at the common center is: 0 i 2 2 R 0 i 2 R 0 i 4 R 2 0 i R A toroid has a core of inner radius 20 cm and outer radius 22 cm, with 500 turns of wire. If the current in the wire is 10 A, the magnetic field at a point in the core is: 4.76 10 -3 T 2.38 10 -3 T 9.52 10 -3 T Zero A long solenoid of length L and radius a has N turns. A current I flows through it. If a second layer of N turns is wound over it in the same direction, the magnetic field at its centre: Doubles Remains same Becomes half Becomes four times A current of 2 A is flowing in a circular loop of radius 0.1 m. The magnetic field at the center of the loop is B 1 . If the same current flows through a square loop of side 0.1 m, the magnetic field at the center is B 2 . The ratio B 1/B 2 is: / (4 2 ) / 4 / 2 2 1 A current I flows in an infinitely long wire with cross-section in the form of a semi-circular ring of radius R . The magnetic field along the axis of the semi-circle is: 0 I / ( 2 R) 0 I / (2 R) 0 I / (4R) 0 I / (2R) The magnetic field at the center of a current-carrying square loop of side 2a is B . The magnetic field at the center of a circular loop of radius a carrying the same current is B' . The ratio B/B' is: 2 2 / 2 / 2 / 4 / A current I 0 flows through a metallic circular loop of radius r as shown in the figure. Resistance of the segment ABC is half that of ADC . Magnitude of magnetic field at the centre O of the loop is: 0 I 0 12r 0 I 0 4r 0 I 0 2r 0 I 0 2 r The magnetic field at the centre of a current carrying circular loop is B . If the current is kept constant and the radius is tripled, the magnetic field at the centre will be: B/3 3B B/9 9B A toroid of inner radius 25 cm and outer radius 26 cm has 3500 turns of wire. If the current in the wire is 11 A, what is the magnetic field in the empty space surrounded by the toroid? 0 T 4.4 10 -2 T 3.0 10 -2 T 1.1 10 -2 T Two parallel wires carry currents I 1 and I 2 in the same direction. The magnetic field at a point exactly midway between them is zero. This implies: I 1 = I 2 I 1 = 2I 2 2I 1 = I 2 I 1 = -I 2 The magnetic field at a distance r from a long straight wire carrying current I is B . The distance at which the field becomes B/4 is: 4r 2r r/4 16r If a solenoid has n turns per unit length and carries a current I , the magnetic field at one of its ends on the axis is: 1 2 0 n I 0 n I 2 0 n I Zero Two long parallel wires are at a distance of 1 m apart. If they carry 1 A current each in the same direction, the force of attraction per unit length between them is: 2 × 10 -7 N/m 2 × 10 -6 N/m 0/4π N/m 10 -7 N/m Which of the following is NOT a unit of magnetic field strength? Wb/m Tesla Gauss N/(A·m) The magnetic field d B at a distance r from a current element Id l depends on r as: 1/r 2 1/r 1/r 3 r 2 The magnetic field at a point on the axis of a long straight current-carrying wire is: Zero Maximum μ 0 I / 2πr μ 0 I / 4πr Which of the following is the correct unit of magnetic flux density? Tesla Weber Weber/metre Tesla-metre A rectangular coil of N turns and area A is placed in a uniform magnetic field B . If the current in the coil is I , the maximum torque on the coil is: NIAB NIAB NIAB IAB The magnetic field at a point P inside a hollow cylindrical conductor carrying current I along its surface is: Zero 0 I / 2 r 0 I / 2r Infinite Gauss's law for magnetism states that the net magnetic flux through any closed surface is: Always zero 0 times the pole strength Non-zero for a dipole Infinite The magnetic field B inside a long solenoid carrying current I is independent of: The radius of the solenoid The current I The number of turns per unit length n The permeability of the core material A magnetic dipole of moment M is kept in a uniform magnetic field B . The potential energy of the dipole is maximum when the angle between M and B is: 180 0 90 45 The unit of magnetic permeability 0 is: T m/A T A/m T/m A T m A The existence of magnetic monopoles is ruled out by: Gauss's Law for Magnetism Ampere's Law Faraday's Law Coulomb's Law The magnetic field lines produced by a long straight current-carrying conductor are: Concentric circles Straight lines parallel to the wire Straight lines perpendicular to the wire Elliptical loops What is the magnetic field at the center of a circular loop of radius R if only three-quarters of the loop carries a current I ? 3 0 I / (8R) 0 I / (2R) 3 0 I / (4R) 0 I / (8R) A current I flows through a long straight conductor. At a distance d from the wire, the magnetic field is 0.4 T. At a distance 2d , the magnetic field will be: 0.2 T 0.1 T 0.8 T 0.4 T A current I flows in a square loop of side L . The magnetic dipole moment of the loop is: IL 2 4IL I/L 2 IL The torque acting on a magnetic dipole of moment M in a uniform magnetic field B is: M B M B B M M B A thin ring of radius R has a charge Q distributed uniformly over it. If the ring rotates with an angular velocity about its axis, the magnetic moment of the ring is: 1 2 Q R 2 Q R 2 Q R 2 1 4 Q R 2 A magnetic dipole is in stable equilibrium in a uniform magnetic field. The work done in rotating it by 180 is: 2MB MB Zero -2MB The magnetic field at a distance r from a long wire carrying current I is 0.4 T. The magnetic field at a distance 2r is: 0.2 T 0.8 T 0.1 T 1.6 T Two bar magnets of same length and same magnetic moment M are joined to form a cross (+ shape). The net magnetic moment of the system is: 2 M 2M M Zero A long solenoid has n turns per unit length and carries a current I . If the solenoid is filled with a material of relative permeability r , the magnetic field inside is: 0 r n I 0 n I r n I 0 n I r The work done in rotating a magnetic dipole of magnetic moment M through an angle 90 ∘ from the direction of a uniform magnetic field B is: MB MB/2 2MB Zero Which of the following units is used to measure magnetic intensity H ? Amperes per metre Tesla Weber Gauss The magnetic intensity H at the center of a long solenoid having n turns per unit length and carrying current I is: nI 0 nI nI / 2 0 I / n A long straight wire of circular cross-section of radius R carries a current I distributed uniformly over its cross-section. The magnetic field B is measured at a distance r from the axis. Which of the following is correct? B = 0 at r = 0 B 1/r for r < R B is maximum at r = 0 B r for r > R The magnetic potential energy of a magnetic dipole of moment M in a uniform magnetic field B is minimum when the angle between M and B is: 0 90 180 45 The dimensions of the quantity 1/ 0 0 are the same as those of: Velocity Acceleration Force Energy The Bohr magneton B is given by: eh/4 m eh/2 m e/2m 2 eh/m The magnetic field at a point P due to a current element Id l is zero if: The angle between d l and the position vector r is 0 or 180 The angle between d l and the position vector r is 90 The current is very high The distance is very small The unit of magnetic intensity H is: Ampere/meter Tesla Weber/meter 2 Ampere-meter A magnetic flux of 500 Wb passes through a closed surface. The net magnetic charge enclosed by the surface is: Zero 500 C 4 10 -7 units Infinite The magnetic field at the center of a circular current-carrying conductor of radius r is B . If the radius is doubled and the current is halved, the new magnetic field at the center will be: B/4 B/2 B 2B If the magnetic dipole moment of an atom of diamagnetic material, paramagnetic material and ferromagnetic material are denoted by d , p and f respectively, then p=0 and f 0 d 0 and p=0 d 0 and f 0 d=0 and p 0 Above Curie temperature:- A ferromagnetic substance becomes paramagnetic A paramagnetic substance becomes diamagnetic A diamagnetic substance becomes paramagnetic A paramagnetic substance becomes ferromagnetic Two concentric circular coils of radii R 1 and R 2 carry currents I 1 and I 2 in opposite directions. The magnetic field at the center is zero if: I 1/I 2 = R 1/R 2 I 1/I 2 = R 2/R 1 I 1 I 2 = R 1 R 2 I 1/I 2 = (R 1/R 2) 2 Nickel shows ferromagnetic property at room temperature. If the temperature is increased beyond Curie temperature, then it will show anti ferromagnetism no magnetic property diamagnetism paramagnetism A bar magnet having a magnetic movement of 2 10 4 JT -1 is free to rotate in a horizontal plane. A horizontal magnetic field B =6 10 -4 T exists in the space. The work done in taking the magnet slowly from a direction parallel to the field to a direction 60 from the field is : 2 J 0.6 J 12 J 6 J If a diamagnetic substance is brought near the north or the south pole of a bar magnet, it is : Attracted by both the poles Repelled by both the poles Repelled by the north pole and attracted by the south pole Attracted by the north pole and repelled by the south pole A current loop in a magnetic field Experiences a torque whether the field is uniform or non uniform in all orientations Can be in equilibrium in one orientation Can be in equilibrium in two orientations, both the equilibrium states are unstable Can be in equilibrium in two orientations, one stable while the other is unstable Following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole moment m . Which configuration has highest net magnetic dipole moment ? (a) (b) (c) (d) The magnetic susceptibility is negative for : diamagnetic material only paramagnetic material only ferromagnetic material only paramagnetic and ferromagnetic materials Two reasons for using soft iron as the material for electromagnets low permeability and high retentivity high permeability and low retentivity low permeability and low retentivity high permeability and high retentivity A thin diamagnetic rod is placed vertically between the poles of an electromagnet. When the current in the electromagnet is switched on, then the diamagnetic rod is pushed up, out of the horizontal magnetic field. Hence the rod gains gravitational potential energy. The work required to do this comes from The lattice structure of the material of the rod The magnetic field The current source The induced electric field due to the changing magnetic field At a point A on the earth’s surface the angle of dip, = +25 . At a point B on the earth’s surface the angle of dip, = -25 . We can interpret that: A and B are both located in the southern hemisphere. A and B are both located in the northern hemisphere. A is located in the southern hemisphere and B is located in the northern hemisphere. A is located in the northern hemisphere and B is located in the southern hemisphere. An iron rod of susceptibility 599 is subjected to a magnetising field of 1200 A m -1 . The permeability of the material of the rod is : ( 0 = 4 10 -7 T m A -1 ) 8.0 10 -5 T m A -1 2.4 10 -5 T m A -1 2.4 10 -7 T m A -1 2.4 10 -4 T m A -1 The magnetic field at a point at distance r from the axis of a long straight wire of radius R is B . If r < R , which of the following is true? B r B 1/r B r 2 B 1/r 2 The net magnetic flux through any closed surface is Zero Positive Infinity Negative Match List-I with List-II. array ll List-I (Material) & List-II (Susceptibility ( )) A. Diamagnetic & I. = 0 B. Ferromagnetic & II. 0 > -1 C. Paramagnetic & III. 1 D. Non-magnetic & IV. 0 < < (a small positive number) array Choose the correct answer from the options given below A-II, B-III, C-IV, D-I A-II, B-I, C-III, D-IV A-III, B-II, C-I, D-IV A-IV, B-III, C-II, D-I A 2 amp current is flowing through two different small circular copper coils having radii ratio 1 : 2 . The ratio of their respective magnetic moments will be 4 : 1 1 : 4 1 : 2 2 : 1 A current-carrying circular loop of radius R carries a current I . The magnetic field at the center of the loop is B . What is the magnetic field at a point on the axis of the loop at a distance x = R from the center? B/2√2 B/2 B/4 B/√2 A circular coil of 100 turns and radius 10 cm carries a current of 0.1 A. The magnetic dipole moment of the coil is: 0.314 Am 2 3.14 Am 2 0.0314 Am 2 31.4 Am 2 The magnetic field at the centre of a circular arc of radius R subtending an angle of 60 ∘ at the centre and carrying current I is: 0 I / 12R 0 I / 6R 0 I / 2R 0 I / 4R The magnetic field inside a long straight solenoid of length L and total turns N carrying current I is B . If the length and the number of turns are both doubled, the magnetic field will be: B 2B B/2 4B A rectangular coil of length 0.12 m and width 0.1 m having 50 turns carries a current of 2 A. It is placed in a uniform magnetic field of 0.2 T. The maximum torque experienced by the coil is: 0.24 Nm 2.4 Nm 0.12 Nm 1.2 Nm A wire of length L is bent into a circular loop and a current I is passed through it. If it is then bent into a coil of two turns and the same current is passed, the magnetic field at the center will: Become 4 times Become 2 times Remain the same Become 1/4 times A thick straight wire of radius R carries a steady current I . The current is uniformly distributed across its cross-section. The ratio of the magnetic field at a distance R/2 and 2R from the axis of the wire is: 1 4 1/4 1/2 According to Ampere's law, for a solenoid of infinite length, the magnetic field at any point outside the solenoid is: Zero Uniform and non-zero Decreasing as 1/r Increasing as r The magnetic field d B due to a current element Id l at a point with position vector r is given by Biot-Savart Law as: d B = 0 4 I (d l r ) r 3 d B = 0 4 I (d l r ) r 2 d B = 0 4 I ( r d l ) r 3 d B = 0 4 I d l r 2 A current of 3 A flows through a circular coil of 100 turns and radius 10 cm. The magnetic field at the center of the coil is: 6 10 -4 T 3 10 -4 T 6 10 -5 T 3 10 -5 T Two long straight parallel wires carry currents I and 2I in the same direction. If the distance between them is d , the magnetic field at the midpoint between them is: 0 I d 3 0 I d 0 I 2 d Zero A circular loop of area A and carrying current I is placed in a magnetic field B such that the plane of the loop is parallel to the field. The torque on the loop is: IAB Zero IAB/2 IAB 0 A long straight wire of radius a carries a steady current i . The current is uniformly distributed across its cross-section. The ratio of the magnetic field at a/2 and 2a is: 1 1/2 1/4 2 A solenoid has a core of material with relative permeability 400. The windings of the solenoid are insulated from the core and carry a current of 2 A. If the number of turns is 1000 per metre, the magnetic field B is: 1.0 T 0.1 T 0.5 T 0.01 T The magnetic field at the center of a circular loop of radius R carrying current I is B c . The magnetic field at a point on its axis at a distance x = R 3 from the center is B a . The ratio B c/B a is: 8 4 2 1/8 A long solenoid has n turns per unit length and carries current i . The magnetic field at a point on the axis at one end of the solenoid is: 1 2 0 ni 0 ni 2 0 ni Zero According to the Biot-Savart law, the magnetic field induction d B at a point due to a current element Id l is given by: d B = 0 4 I(d l r ) r 3 d B = 0 4 I(d l r ) r 2 d B = 0 4 I(d l r ) r 3 d B = 0 4 I(d l r ) r Two circular coils of radius R are placed such that their centers coincide and their planes are perpendicular to each other. If each coil carries current I , the net magnetic field at the center is: 0 I 2 R 0 I 2R 2 0 I R 0 I R The magnetic field B inside a long solenoid carrying current I is B = 0 n I . This formula is NOT valid: Near the ends of the solenoid At the center of the solenoid When I is very large When n is very large The magnetic field at a point due to a semi-infinite long straight wire carrying current I at a perpendicular distance R from its end is: 0 I 4 R 0 I 2 R 0 I R Zero A long solenoid has 1000 turns. When a current of 4 A flows through it, the magnetic flux linked with each turn of the solenoid is 4 10 -3 Wb. The self-inductance of the solenoid is: 1 H 4 H 3 H 2 H A circular arc of wire of radius R subtends an angle /2 at the centre. If it carries a current I , the magnetic field at the centre is: 0 I 8R 0 I 4R 0 I 2R 0 I 16R A solenoid of length 0.5 m has a radius of 1 cm and is made up of 500 turns. It carries a current of 5 A. The magnitude of the magnetic field inside the solenoid is: 6.28 10 -3 T 3.14 10 -3 T 9.42 10 -3 T 1.25 10 -2 T A wire of length L carries a steady current I . It is bent first into a circular loop of one turn and then into a circular coil of n turns. If the same current is passed in both cases, the ratio of the magnetic field at the center of the loop to that at the center of the coil is: 1 : n 2 n 2 : 1 1 : n n : 1 The magnetic field at a distance r from the axis of a long straight wire of radius a carrying a steady current I (uniformly distributed) is proportional to: r for r < a and 1/r for r > a 1/r for r < a and r for r > a r 2 for r < a and 1/r 2 for r > a 1/r 2 for r < a and r 2 for r > a A long solenoid has 1000 turns per metre. It has a core of material with relative permeability 500 . If a current of 2 A is passed through it, the magnetic intensity H and magnetic field B inside the solenoid are respectively: 2000 A/m, 1.26 T 1000 A/m, 0.63 T 2000 A/m, 0.63 T 1000 A/m, 1.26 T A long solenoid has 500 turns. When a current of 2 A is passed through it, the resulting magnetic flux linked with each turn of the solenoid is 4 10 -3 Wb. The self-inductance of the solenoid is: 1.0 H 2.5 H 2.0 H 4.0 H Two long parallel wires P and Q are held perpendicular to the plane of the paper with a distance of 5 m between them. If P and Q carry current of 2.5 A and 5 A respectively in the same direction, then the magnetic field at a point midway between the wires is: 2 10 -7 T 6 10 -7 T 1.2 10 -6 T 0 A long straight wire of radius R carries a steady current I . The current is uniformly distributed across its cross-section. The ratio of the magnetic field at distance r = R/3 and r = 3R from the axis is: 1:1 1:3 3:1 1:9 Two long parallel wires carry currents I 1 and I 2 such that I 1 = 2 I 2 in the same direction. If the force per unit length on wire 1 is F , the force per unit length on wire 2 is: F 2F F/2 Zero A long solenoid has a core of material with relative permeability 200 . If the current in the solenoid is 1 A and it has 500 turns per meter, the magnetic field B inside is: 4 10 -2 T 2 10 -3 T 8 10 -5 T 4 10 -4 T The magnetic field inside a long straight wire of radius a at a distance r < a from its axis is proportional to: r 1/r r 2 1/r 2 A circular coil of radius R carries a current I . The ratio of the magnetic field at the center of the coil to that at a point on its axis at a distance x = R from the center is: 2 2 2 2 4 A square loop of side a carries a current I . The magnetic field at the center of the loop is B . If the side of the square is doubled to 2a and the current is halved to I/2 , the new magnetic field at the center will be: B/4 B/2 B/8 2B The horizontal component of the Earth's magnetic field at a certain place is 3 10 -5 T and the direction of the field is from geographic south to north. A very long straight conductor is carrying a steady current of 1 A. The force per unit length on it when it is placed on a horizontal table and the direction of the current is east to west is: 3 10 -5 N/m 3 10 -4 N/m Zero 1.5 10 -5 N/m A thick current-carrying cable of radius R carries a current I uniformly distributed across its cross-section. Which graph correctly represents the variation of the magnetic field B with the distance r from the axis of the cable? B r for r < R and B 1/r for r > R B = 0 for r < R and B 1/r for r > R B r 2 for r < R and B 1/r 2 for r > R B is constant for r < R and B 1/r for r > R Two toroids 1 and 2 have total number of turns 200 and 100 respectively with average radii 40 cm and 20 cm respectively. If they carry the same current I , the ratio of the magnetic fields along the two loops is: 1:1 1:2 2:1 4:1 The magnetic field due to a straight current carrying conductor of finite length L at a distance d on its perpendicular bisector is given by: ( 0 I / 2 d) ( 0 I / 4 d) ( 0 I / 2 d) ( 0 I / d) A long solenoid has 1000 turns per metre and carries a current of 1 A. If the solenoid is filled with a material of magnetic susceptibility = 499 , the magnetic field inside is: 0.628 T 0.314 T 0.012 T 1.256 T A solenoid of length L has N turns and carries a current I . If the wire is unwound and rewound into a solenoid of length L/2 with the same number of turns, the magnetic field inside (for the same current I ): Doubles Remains same Becomes half Becomes four times