First slide

Magnetic field due to current element

Question

Magnitude of magnetic field (in SI units at the center of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of $\frac{μ_{0} I}{π}$ is :

Moderate

A

$50 \sqrt{3}$
B

$500 \sqrt{3}$
C

$250 \sqrt{3}$
D

$5 \sqrt{3}$

Solution

Magnetic field due to one side at center is
$\begin{array}{l} B = \frac{μ_{0} i}{4 π r} (\sin α + \sin β) = \frac{μ_{0} i}{4 π (\frac{\sqrt{3} a}{2})} (\sin 30 º + \sin 30 º) = \frac{μ_{0} i}{2 π \sqrt{3} a} \\ T h e r e a r e 6 s i d e s a n d 50 t u r n s \\ B = 6 \times 50 \times \frac{μ_{0} i}{2 π \sqrt{3} (0.1)} = 500 \sqrt{3} \frac{μ_{0} i}{π} \end{array}$

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