Question

A closed loop carrying current I lies in the x-z plane. The loop will experience a force if it is placed in a region occupied by a uniform magnetic field along:
A. x-axis
B. y-axis
C. z-axis
D. none of these

Answer 1

The loop will experience a force if it is placed in a region occupied by a uniform magnetic field along none of the directions, as, in the uniform magnetic field, the force on any current carrying loop is always zero.

Complete step by step answer:
From the given information, we have the data as follows.
A closed loop carrying current I lies in the x-z plane. We are asked to find the direction along which the closed loop should be placed in a region occupied by a uniform magnetic field that experiences a force.
Now consider the general situation.
If the current I is flowing on a closed contour C, the total magnetic force becomes.
$F=I\oint\limits_{C}{dl\times B}$
Where I is the current, B is the magnetic field and dl is the small length.
As the magnetic field is constant, so, we have to take it out of the integral.

& F=I\left( \oint\limits_{C}{dl} \right)\times B \\\ & \therefore F=I\left( \oint\limits_{C}{dl} \right)\times B \\\ \end{aligned}$$ The closed integral of the small length becomes zero, so, we get, $$\begin{aligned} & F=I\left( 0 \right)\times B \\\ & \therefore F=0 \\\ \end{aligned}$$ The loop will experience a force if it is placed in a region occupied by a uniform magnetic field along none of the directions, as, in the uniform magnetic field, the force on any current carrying loop is always zero. In the uniform magnetic field, the force on any current carrying loop is always zero. **So, the correct answer is “Option D”.** **Note:** The loop will experience a force if it is placed in a region occupied by a uniform magnetic field along none of the directions, as, in the uniform magnetic field, the force on any current carrying loop is always zero.