First slide

Magnetic field due to current element

Question

Three rings each having equal radius R are placed mutually perpendicular to each other and each having its center at the origin of co-ordinates system. If current I is flowing through each ring then the magnitude of the magnetic field at the common center is

Moderate

A

$\sqrt{3} \frac{μ_{o} I}{2 R}$
B

$Z e r o$
C

$(\sqrt{2} - 1) \frac{μ_{o} I}{2 R}$
D

$(\sqrt{3} - \sqrt{2}) \frac{μ_{o} I}{2 R}$

Solution

$F i e l d a t c e n t e r o f c u r r e n t c a r r y i n g l o o p = \frac{μ_{o} i}{2 R} ∴ {\vec{B}}_{n e t} = B_{1} \hat{i} + B_{2} \hat{j} + B_{3} \hat{k} = \frac{μ_{o} i}{2 R} \hat{i} + \frac{μ_{o} i}{2 R} \hat{j} + \frac{μ_{o} i}{2 R} \hat{k} M a g n i t u d e o f {\vec{B}}_{n e t} = \sqrt{3} \frac{μ_{o} i}{2 R}$

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