Question

A particle of mass \( m \) and charge \( q \) moves along the y-axis in a region in which a uniform magnetic field \( \vec{B} \) is pointing along the x-axis. The Lorentz force acting on the charge will point along:

• A. x-axis
• B. y-axis
• C. z-axis
• D. negative z-axis

Hint:

The direction of the magnetic force is determined using the right-hand rule: point your fingers in the direction of the velocity, curl them towards the magnetic field, and your thumb points in the direction of the force.

Answer 1

The Correct Option is D

The Lorentz force on a charged particle moving in a magnetic field is given by the equation: \[ \vec{F} = q \left( \vec{v} \times \vec{B} \right) \] where: - \( q \) is the charge, - \( \vec{v} \) is the velocity of the particle, - \( \vec{B} \) is the magnetic field. Given: - The particle moves along the \( y \)-axis, so the velocity is \( \vec{v} = v_y \hat{j} \), - The magnetic field \( \vec{B} \) is along the \( x \)-axis, so \( \vec{B} = B_x \hat{i} \). Now, applying the cross product: \[ \vec{F} = q \left( v_y \hat{j} \times B_x \hat{i} \right) \] Using the right-hand rule for the cross product \( \hat{j} \times \hat{i} = -\hat{k} \), we get: \[ \vec{F} = -q v_y B_x \hat{k} \] This means the force is acting along the negative \( z \)-axis. Hence, the correct answer is: \[ \boxed{D} \text{ negative z-axis} \]