Question

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is:
A. Away from the wire
B. Parallel to the wire along the current
C. Towards the wire
D. Parallel to the wire opposite to the current

Answer 1

Hint: Look at the direction of the current flowing in the wire and the motion of the particle. Apply Fleming’s left hand thumb rule to find the direction of the magnetic field at a point nearby the charge. Then find the vector product to find the resultant direction of the motion of the particle.

Complete step by step answer:
It is given that a negative charge is moving near a long straight wire carrying a current. Let I be the current flowing through the wire along the y-axis and the charge is moving towards the wire along the x-axis. Let A be a point in the vicinity of the wire and the test charge. Then according to Fleming’s left hand thumb rule the direction of the magnetic field at point A will be along the z-axis, that is out of the plane of the paper. The intensity of the magnetic field at A is given by $$\overrightarrow{B}=B_0\times \hat{k}$$ , where $$\hat{k}$$ is the unit vector along the z-axis. If $$\overrightarrow{v}$$ is the velocity vector, then
The force acting on the test charge is given by
$$\overrightarrow{F}=-q\times \overrightarrow{v}\times \overrightarrow{B}$$
$$\Rightarrow \overrightarrow{F}=-q\times v\times \hat{x}\times B_0\times \hat{k}$$
As the vector product of $$\hat{x}\times \hat{k}$$ is $$-\hat{j}$$.
Therefore, $$\overrightarrow{F}=+q\times v\times B_0\times \hat{j}$$
Therefore, the particle will move towards the wire.

So, the correct answer is “Option C”.

Note:
According to Fleming’s left hand rule, if we stretch the first finger, the middle finger and the thumb of left mutually perpendicular to each other such that the first finger points towards the direction of the magnetic field, the central finger points to the direction of the electric current, then the thumb points the direction of the force experienced by the charged particle.