Two concentric coils each of radius equal to 2π cm are placed at right angles to each other. 3 Ampere and 4 am

Question

Two concentric coils each of radius equal to 2π 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 = 4π × 10^-7 W/A-m):

Accepted Answer

1. Magnetic field at the centre of a coil

B = \frac{μ _{0} i}{2 r}

.

r = 2 π cm = 0.02 π m

.

B_{1} = \frac{4 π \times 1 0 ^{- 7} \cdot 3}{2 ( 0.02 π )} = \frac{6 \times 1 0 ^{- 7}}{0.02} = 3 \times 1 0^{- 5} T

.

B_{2} = \frac{4 π \times 1 0 ^{- 7} \cdot 4}{2 ( 0.02 π )} = \frac{8 \times 1 0 ^{- 7}}{0.02} = 4 \times 1 0^{- 5} T

.2. Since the coils are at right angles, their fields are also at right angles (

B_{n e t} = B_{1}^{2} + B_{2}^{2}

).

B_{n e t} = (3 \times 1 0^{- 5})^{2} + (4 \times 1 0^{- 5})^{2} = 5 \times 1 0^{- 5} T

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 ( $μ_{0} = 4 π \times 1 0^{- 7}$ W/A-m):

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Two concentric coils each of radius equal to 2π 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/m2 at the centre of the coils will be (μ0​=4π×10−7 W/A-m):