An electron is moving along the positive x-axis. If the 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 options given below:

Solution

Physics sir · 4 steps

Do the cross product for a positive charge first, then flip the direction because the electron is negative.

1. Set up the force. The magnetic force is F⃗ = q v⃗ × B⃗. Here v⃗ = v î, B⃗ = -B k̂ and q = -e.

   F⃗ = (-e)(v î × (-B k̂)) = (-e)(vB ĵ) = -evB ĵ

2. Direction of force. Since î × k̂ = -ĵ, we get î × (-k̂) = +ĵ. The negative charge reverses this, so the force is along the negative y-axis. Statement B is true and A is false.
3. Path of the electron. The velocity is perpendicular to the field, so the force is not zero, and C is false. The force always stays perpendicular to the velocity and has constant size evB. It bends the electron into a circular path, so E is true and D is false.
4. So. Only B and E are correct, which is option (c).

The idea to keep. For an electron, find the direction of v⃗ × B⃗ and then reverse it. If v⃗ is perpendicular to a uniform B⃗, the path is always a circle.

Answer from the NTA final answer key. Solution by PrepWiser.