JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Magnetic Effects of Current

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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:

(A) $6 : 5$ ✓ Correct
(B) $2 : 5$
(C) $6 : 4$
(D) $4 : 6$

Answer: (A)

Solution

The field at the common centre from a circular arc is

B = \frac{μ _{0} I θ}{4 π R}

, where

θ

is the angle the arc subtends there. Taking the ratio for the two wires,

\frac{B _{A}}{B _{B}} = \frac{I _{A} θ _{A} R _{B}}{I _{B} θ _{B} R _{A}}

. With

I_{A} = 2

A and

R_{A} = 2

cm subtending

θ_{A} = \frac{3 π}{2}

, and

I_{B} = 3

A and

R_{B} = 4

cm subtending

θ_{B} = \frac{5 π}{3}

\frac{B _{A}}{B _{B}} = \frac{2 \cdot \frac{3 π}{2} \cdot 4}{3 \cdot \frac{5 π}{3} \cdot 2} = \frac{12 π}{10 π} = \frac{6}{5}

, a ratio of

6 : 5

JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Single correct option

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JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Magnetic Effects of Current

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