An electron is moving along the positive x-axis. If uniform magnetic field is applied parallel to the negative z-axis, then
A. The electron will experience magnetic force along positive y-axis
B. The electron will experience magnetic force along negative y-axis
C. The electron will not experience any force in magnetic field
D. The electron will continue to move along the positive x-axis
E. The electron will move along circular path in magnetic field
Choose the correct answer from the option given below:

An electron has negative charge $$q = -e$$. The magnetic (Lorentz) force on a moving charge is given by
$$\mathbf{F}=q\,(\mathbf{v}\times\mathbf{B})$$

Velocity of the electron: $$\mathbf{v}=v\,\hat{i}$$ (along the +x-axis).
Magnetic field applied: $$\mathbf{B}=-B\,\hat{k}$$ (along the −z-axis).

First evaluate the cross product for a positive charge:
$$\mathbf{v}\times\mathbf{B}=v\hat{i}\times(-B\hat{k})$$
$$= -vB(\hat{i}\times\hat{k})$$

Using the right-hand rule for unit vectors, $$\hat{i}\times\hat{k}=-\hat{j}$$. Hence
$$\mathbf{v}\times\mathbf{B}=-vB(-\hat{j})=vB\,\hat{j}$$ (towards +y).

For an electron, multiply by $$q=-e$$:
$$\mathbf{F}=-e(vB\,\hat{j})=-evB\,\hat{j}$$

Therefore the magnetic force is along the negative y-axis. Statement B is correct, while statement A is incorrect.

The velocity is perpendicular to the magnetic field ( $$\mathbf{v}\perp\mathbf{B}$$ ), so the electron undergoes uniform circular motion in the plane perpendicular to $$\mathbf{B}$$ with constant speed and radius $$r=\dfrac{mv}{eB}$$. Hence statement E is also correct.

Statements C (no force) and D (continues along +x) are wrong.

The correct set of statements is B and E only → Option C.