Two long parallel conductors $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure). A charge particle of $3 \pi$ coulomb is passing through the point P with velocity $\overrightarrow{\mathrm{v}}=(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s}$; where $\hat{\mathrm{i}} \& \hat{\mathrm{j}}$ represents unit vector along $\mathrm{x} \& \mathrm{y}$ axis respectively. The force acting on the charge particle is $4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) \mathrm{N}$. The value of $x$ is :

JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Magnetic Effects of Current

Two long parallel conductors

S_{1}

and

S_{2}

are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure).

A charge particle of

3 π

coulomb is passing through the point P with velocity

v = (2 \hat{i} + 3 \hat{j}) m / s

; where

\hat{i} & \hat{j}

represents unit vector along

x & y

axis respectively.

The force acting on the charge particle is

4 π \times 1 0^{- 5} (- x \hat{i} + 2 \hat{j}) N

. The value of

x

is :

(A)2
(B)1
(C)3✓ Correct
(D)-3

Answer: (C)

Solution

The magnetic field at point P is the vector sum of fields from both conductors. At distance 4 cm from

S_{1}

and 6 cm from

S_{2}

B_{net} = B_{1} - B_{2} = \frac{μ _{0} \times 4}{2 π ( 0.04 )} - \frac{μ _{0} \times 2}{2 π ( 0.06 )} = \frac{μ _{0}}{2 π} (\frac{200}{3}) (- \hat{k})

The magnetic force is:

F = q (v \times B) = 3 π [(2 \hat{i} + 3 \hat{j}) \times \frac{μ _{0}}{2 π} \cdot \frac{200}{3} (- \hat{k})]

= 3 π \times \frac{μ _{0}}{2 π} \times \frac{200}{3} [2 \hat{j} - 3 \hat{i}]

= 4 π \times 1 0^{- 7} \times 100 (- 3 \hat{i} + 2 \hat{j}) = 4 π \times 1 0^{- 5} (- 3 \hat{i} + 2 \hat{j})

Therefore,

x = 3

JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Single correct option

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JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Magnetic Effects of Current

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