First slide

Magnetic field due to current element

Question

A wire A, bent in the shape of an arc of a circle, carrying a current of 2 A and having radius 2 cm and another wire B, also bent in the shape of arc of a circle, carrying a current of 3 A and having radius of 4 cm, are placed as shown in the figure. The ratio of the magnetic fields due to the wires A and B at the common centre O is :

Moderate

A

6 : 5
B

4 : 6
C

6 : 4
D

2 : 5

Solution

Magnetic field due to arc of circular current $= (\frac{θ}{360 °}) \frac{μ_{0} i}{2 R}$ at the center.
Here required ratio $= \frac{B_{A}}{B_{B}} = \frac{θ_{A} i_{A} / R_{A}}{θ_{B} i_{B} / R_{B}} = \frac{270}{300} \times \frac{2}{3} \times \frac{4}{2} = \frac{6}{5}$

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