First slide

Magnetic field due to a current carrying circular ring

Question

Two concentric coils each of radius equal to $2 π$ cm are placed at right angles to each other. 3 A and 4 A are the current, flowing in each coil, respectively. The magnetic induction, in Wb/m², at the centre of the coils will be $(μ_{0} = 4 π \times 10^{- 7} Wb / A . m)$

Moderate

A

$5 \times 10^{- 5}$
B

$7 \times 10^{- 5}$
C

$12 \times 10^{- 5}$
D

$10^{- 5}$

Solution

$\begin{array}{l} B_{net} = \sqrt{B_{1}^{2} + B_{2}^{2}} = \frac{μ_{0}}{4 π} . \frac{2 π}{r} \sqrt{i_{1}^{2} + i_{2}^{2}} \\ = 10^{- 7} \times \frac{2 π}{2 π \times 10^{- 2}} \sqrt{{(3)}^{2} + {(4)}^{2}} \\ = 5 \times 10^{- 5} Wb / m^{2} \end{array}$

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