Question

Current ${I_0}$ flows through the solenoid of length $L$ having $N$ number of turns when it is connected to DC. A charged particle is projected along the axis of the solenoid with a speed ${v_0}$, then the force on the charged particle in the solenoid
A. Becomes zero
B. Remains same
C. Decreases
D. Increases

Answer 1

To solve this question, we first need to understand about the force acting on a charge having particular velocity and magnetic field which is known as Lorentz force. The direction of the projection of a charged particle is given in the question. According to this, we will find the magnitude of force.

Formula used:
$F = q(v \times B)$,
where, $F$ is the force on the charged particle in the solenoid, $q$ is the charge, $v$ is the speed of the projected charged particle and $B$ is the magnetic field.

Complete step by step answer:
Let us consider a charge $q$ is projected along the axis of the solenoid with a speed ${v_0}$ in a magnetic field $B$. Therefore, the force on the charged particle in the solenoid is given by the Lorentz force:
$F = q({v_0} \times B)$
In a solenoid, the magnetic field is along the axis of the solenoid. Also, we are given that a charged particle is projected along the axis of the solenoid. This means that both magnetic field and speed are parallel to each other and hence the angle between them is zero degree.
Therefore, the magnitude of the force is given by:
$F = q(\left| {{v_0}} \right| \times \left| B \right|)\sin 0^\circ = 0N$
Thus, the force on the charged particle in the solenoid becomes zero.

Hence, option A is the right answer.

Note: In this question, we have seen that there is a uniform magnetic field inside solenoid which is parallel or anti parallel to the magnetic field depending on direction of current. We are given that the charged particle has been projected along the axis of the solenoid and hence the direction of motion of the charged particle is along or anti parallel to the direction of the magnetic field. Using this concept, we have determined that the force on the charged particle in the solenoid in this case becomes zero.