Magnetic Field Inside A Toroid — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Magnetic Field inside a Toroid Consider the toroid as a solenoid bent into a circular shape. Apply Ampere's Circuital Law: B d l = 0 I enclosed . Choose a circular Amperian loop of radius r inside the toroid (concentric with the toroid). Assume symmetry where B is constant in magnitude along the loop and tangent to the circle. Evaluate the line integral: B dl = B(2 r) . Calculate enclosed current: The loop encloses N turns, each carrying current I , so I enclosed = NI . Equate sides: B(2 r) = 0 N I . Solve for B: B = 0 N I 2 r . Confusing total turns N with turns per unit length n . Note that n = N 2 r . Assuming the magnetic field is non-zero inside the hollow center (the hole) of the toroid. Assuming the magnetic field is non-zero outside the toroid. Assuming the field is perfectly uniform inside the toroid (it actually varies slightly with radius 1/r , but is approximated as uniform for thin cores).