Question

Consider the specific example of a positive charge q moving in the +x direction with the local magnetic field in the +y direction. In which direction is the magnetic force acting on the particle? Express your answer using unit vectors (e.g., i^- j^). (Recall that i^ is written \hat i (or alternatively i_unit can be used.))

Answer 1

Answer:

z+ direction

Explanation:

Imagine x+ and y+ as normal coordinate system on a paper. By using the right hand rule with thumb pointing to the direction of charge q moving (x+) and fingers pointing in the direction of the magnetic field (y+). The direction of the magnetic force would be coming out of your palm, or out of the paper surface in the z+ direction.

Answer 2

Answer:

Therefore the direction is in the positive direction of the z axes.

Explanation:

Let's recall that the magnetic force is given by:

$F_{B}=q(\vec{v} \times \vec{B})$

The unit vector of V is $\hat{i}$ and the unit vector of B is $\hat{j}$

So, the direction of the force will be defined as the cross product of i and j, and using the right hand rule:

$\hat{i} \times \hat{j} = \hat{z}$

Therefore the direction of the magnetic force is in the positive direction of the z axes.

I hope it helps you!