JEE Main · 2005 · 08 May 2005 · Offline · Magnetic Effects of Current

Two concentric coils each of radius equal to

2 π cm

are placed at right angles to each other. 3 Ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber

/ m^{2}

at the centre of the coils will be (

μ_{0} = 4 π \times 1 0^{- 7}

Wb/A-m)

Answer: (C)

Solution

Each coil makes a field

B = \frac{μ _{0} I}{2 r}

at the shared centre, and because the coils are at right angles their fields are perpendicular and combine as vectors:

B = \frac{μ _{0}}{2 r} I_{1}^{2} + I_{2}^{2}

. With

r = 2 π \times 1 0^{- 2}

\frac{μ _{0}}{2 r} = \frac{4 π \times 1 0 ^{- 7}}{4 π \times 1 0 ^{- 2}} = 1 0^{- 5}

, so

B = 1 0^{- 5} 3^{2} + 4^{2} = 1 0^{- 5} \times 5 = 5 \times 1 0^{- 5}

Wb/m

^{2}

JEE Main · 2005 · 08 May 2005 · Offline · Single correct option