A charge of $4.0 \mu \mathrm{C}$ is moving with a velocity of $4.0 \times 10^{6} \mathrm{~ms}^{-1}$ along the positive y-axis under a magnetic field $\overrightarrow{\mathrm{B}}$ of strength $(2 \hat{\mathrm{k}})$ T. The force acting on the charge is $x \hat{i} \mathrm{~N}$. The value of $x$ is ______.

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Magnetic Effects of Current

A charge of

4.0 μ C

is moving with a velocity of

4.0 \times 1 0^{6} ms^{- 1}

along the positive y-axis under a magnetic field

B

of strength

(2 \hat{k})

T. The force acting on the charge is

x \hat{i} N

. The value of

x

is ______.

Answer: 32

Solution

The magnetic force on a moving charge is

F = q (v \times B)

. With

q = 4 \times 1 0^{- 6}

v = 4 \times 1 0^{6} \hat{j}

m/s,

B = 2 \hat{k}

F = 4 \times 1 0^{- 6} (4 \times 1 0^{6} \hat{j} \times 2 \hat{k}) = 4 \times 1 0^{- 6} \times 8 \times 1 0^{6} (\hat{j} \times \hat{k})

Since

\hat{j} \times \hat{k} = \hat{i}

F = 32 \hat{i} N

x = 32

JEE Main · 2024 · 29 Jan 2024 · Shift 2 · Integer answer

Practise more: all JEE Main PYQs on Magnetic Effects of Current →

More JEE Main questions on Magnetic Effects of Current

An infinitely long straight wire carrying current I is bent in a planer shape as shown in the diagram. The radius of the circular part is r . The magnetic field at the centre O of the circular loop is :
JEE Main 2026View solution →
The current passing through a conducting loop in the form of equilateral triangle of side $43 cm$ is 2A. The magnetic field at its centroid is $α \times 1 0^{- 5} T$ . The value of $α$ is ____.
(Given : …
JEE Main 2026View solution →
Three long straight wires carrying current are arranged mutually parallel as shown in the figure. The force experienced by 15 cm length of wire $Q$ is ______.
( $μ_{0} = 4 π \times 1 0^{- 7} T . m / A$ )
JEE Main 2026View solution →
The magnetic field at the centre of a current carrying circular loop of radius $R$ is $16 μ T$ . The magnetic field at a distance $x = 3 R$ on its axis from the centre is ____ $μ T$ .
JEE Main 2026View solution →
Two identical circular loops P and Q each of radius r are lying in parallel planes such that they have common axis. The current through P and Q are I and 4I respectively in clockwise direction as seen from O. The net magnetic field at O is:
JEE Main 2026View solution →
A long cylindrical conductor with large cross section carries an electric current distributed uniformly over its cross-section. Magnetic field due to this current is :
A. maximum at either ends of the conductor and minimum at the midpoint
B. maximum at the axis of the conductor
C …
JEE Main 2026View solution →