First slide

Magnetic field due to a current carrying circular ring

Question

Figure shows a coil of radius 2 cm concentric with a coil of radius 7 cm. Each coil has 1000 turns' With a current of 5 amp in larger coil, find the current needed in the smaller coil to give the total magnetic field at the centre equal to 2 mT

Moderate

A

0.793A
B

1 44A
C

2.88A
D

3.4A

Solution

Let B₁and B₂ be the magnetic fields at centres due to bigger and smaller coils. Therefore,
$B_{1} = \frac{μ_{0} {ni}_{1}}{2 r_{1}} = \frac{4 π \times 10^{- 7} \times 100 \times 5}{2 \times 0 .07} = 4 .49 mT$
and $B_{2} = \frac{μ_{0} {ni}_{2}}{2 r_{2}} = \frac{4 π \times 10^{- 7} \times 100 \times i_{2}}{2 \times 0 \cdot 02}$
$\begin{array}{l} B_{1} - B_{2} = 2 or B_{2} = 4 .49 - 2 = 2 .49 mT \\ ∴ 2 \cdot 49 = \frac{4 π \times 10^{- 7} \times 100 \times i_{2}}{2 \times 0 \cdot 02} \\ i_{2} = 0 .793 amp \end{array}$

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