Question: A charge particle is released from rest in a region of uniform electric and magnetic fields which ar...

Question

A charge particle is released from rest in a region of uniform electric and magnetic fields which are parallel to each other. The particle will move on a
A. Straight line
B. Circle
C. Helix
D. Cycloid

Answer 1

Solution

The force acting on the particle is due to the electric field and magnetic field. Electric field provides the particle acceleration and magnetic field provides necessary centripetal force. Which in combination rotates the particle and forms helix motion. We will solve this question with the help of vector analysis.

Complete step by step answer:
We know that the combined force on a charged particle due to electric field and magnetic field is given by:
$F = qE + qvB\sin \theta$
Here, F is the force, q is the charge on the particle. v is the velocity of the particle, B is the magnetic field and $\theta$ is the angle between the velocity and magnetic field.
Here the particle is released parallel to the electric and magnetic field and therefore $\theta = 0^\circ$ . Therefore, the above equation becomes,
$\begin{array}{l} F = qE + qvB\sin 0^\circ \\\ = qE \end{array}$
Hence the charged particle will move parallel to the electric field and in a straight line and the correct option is (A).

Additional Information: The electric field is that region where we can observe that the electric charge is experiencing some electric force. Due to the electric force's effect, the electric field's motion gets affected, and the charge tends to change its state of motion. The magnetic field is the space around the current-carrying conductor around which we can experience magnetic effects. It can also affect the motion of the electric charge.

Note: Force acting on charged particle due to magnetic field is known as Lorentz force which acts normal to the velocity of the particle and magnetic field, because Lorentz force is given by $\overrightarrow F = q\left( {\overrightarrow v \times \overrightarrow B } \right)$ . If the question has vector notation carefully look in which direction the given quantity is acting and then execute the solution.