First slide

Magnetic field due to a current carrying circular ring

Question

A current I flowing through the loop as shown in figure. The magnetic field at centre O is :

Moderate

A

$\frac{7 μ_{0} I}{16 R} \otimes$
B

$\frac{7 μ_{0} I}{16 R} ⊙$
C

$\frac{5 μ_{0} I}{16 R} \otimes$
D

$\frac{5 μ_{0} I}{16 R} ⊙$

Solution

The effective magnetic field at O
$B = B_{P E} + B_{R S} = \frac{μ_{0}}{4 π} \cdot \frac{3}{2} \frac{π I}{R} + \frac{μ_{0}}{4 π} \cdot \frac{π}{2} . \frac{I}{2 R}$
$\Rightarrow B = \frac{μ_{0} I}{4 R} [\frac{3}{2} + \frac{1}{4}] = \frac{7}{16} \frac{μ_{0} I}{R}$
As per Fleming's Right Hand rule, direction of magnetic filed is perpendicular and in the plane of paper.

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