COMEDK2024Evening ShiftPhysicsMagnetic Effects of CurrentActual
A current I flows in an infinitely long wire with cross section in the form of semi-circular ring of radius 1 ~m . The magnitude of the magnetic induction along its axis is
Options
- A₀ I 2 T
- B₀ I 2 ^2 ~T
- C₀ I ^2 ~T
- D₀ I 4 ^2 ~T
Correct answer
C. ₀ I ^2 ~T
Step-by-step solution
Current per unit angle: dI = I d Magnetic field due to element (infinite wire) at axis (distance R ): dB = ₀ dI 2 R = ₀ I 2 ^2 R d By symmetry, only sine components add up: B_ net = ₀^ dB = ₀^ ₀ I 2 ^2 R , d = ₀ I 2 ^2 R [- ]₀^ = ₀ I 2 ^2 R [1+1] = ₀ I ^2 R For R = 1 m: B_ net = ₀ I ^2 T