First slide

Magnetic field due to current element

Question

Calculate the magnetic field at point ‘O’ in the following case.

Moderate

A

$B = \frac{3 μ_{0} i}{8 R} \otimes$
B

$B = \frac{3 μ_{0} i}{4 R} \otimes$
C

$B = \frac{5 μ_{0} i}{4 R} ⊙$
D

$B = \frac{2 μ_{0} i}{3 R} ⊙$

Solution

The magnetic field due to straight wires will be zero.
Magnetic field due to circular part.
$B_{circular} = \frac{μ_{0} i}{2 R} (\frac{θ}{2 π}) = \frac{μ_{0} i}{2 R} (\frac{(3 / 2) π}{2 π}) = \frac{3 μ_{0} i}{8 R} \otimes$

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