First slide

Magnetic field due to a current carrying circular ring

Question

For c = 2a, and a < b < c, the magnetic field at point P will be zero when

Moderate

A

a = b
B

$a = \frac{3}{5} b$
C

$a = \frac{5}{3} b$
D

$a = \frac{1}{3} b$

Solution

Magnetic field at centre,
$B = \frac{μ_{0} I}{2 c} \otimes + \frac{μ_{0} I}{2 b} (\frac{3}{4}) ⊙ + \frac{μ_{0} I}{2 a} (\frac{3}{4}) \otimes$
As per problem,
$\begin{array}{l} 0 = \frac{μ_{0} I}{2} [\frac{1}{c} - \frac{3}{4 b} + \frac{3}{4 a}] \\ If c = 2 a, \\ \frac{5}{4 a} - \frac{3}{4 b} = 0 \Rightarrow a = \frac{5}{3} b \end{array}$

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