Question

An electron is moving along positive x direction in xy plane, magnetic field points in negative z direction, then the force due to magnetic field on electron points in the direction 

• A. j
• B. -j
• C. k
• D. -k

Answer 1

The Correct Option is B

To determine the direction of the force on an electron moving in a magnetic field, we use the principle of the magnetic force acting on a charged particle, given by the Lorentz force formula:

\(\mathbf{F} = q(\mathbf{v} \times \mathbf{B})\)

where:

• \(\mathbf{F}\) is the force on the particle,
• \(q\) is the charge of the particle,
• \(\mathbf{v}\) is the velocity of the particle,
• \(\mathbf{B}\) is the magnetic field.

We need to determine the cross product \(\mathbf{v} \times \mathbf{B}\). Given:

• The velocity \(\mathbf{v} = v \mathbf{i}\) (positive x direction),
• The magnetic field \(\mathbf{B} = -B \mathbf{k}\) (negative z direction).

The cross product is calculated as follows:

\(\mathbf{v} \times \mathbf{B} = (v \mathbf{i}) \times (-B \mathbf{k}) = vB (\mathbf{i} \times -\mathbf{k})\).

Using the right-hand rule for cross products, \(\mathbf{i} \times \mathbf{k} = \mathbf{j}\). Therefore:

\(\mathbf{v} \times \mathbf{B} = vB (-\mathbf{j}) = -vB \mathbf{j}\).

Now, since the electron has a negative charge (\(q = -e\)), the direction of the force \(q(\mathbf{v} \times \mathbf{B})\) is opposite to the direction of \(\mathbf{v} \times \mathbf{B}\):

\(\mathbf{F} = -e(-vB \mathbf{j}) = evB \mathbf{j}\).

This means the direction of the force on the electron is in the negative y-direction (\(-\mathbf{j}\)).

Thus, the force due to the magnetic field on the electron points in the negative y-direction, corresponding to the option -j.