Question

Each of the lettered points at the corners of the cube in Fig. Q27.12 represents a positive charge q moving with a velocity of magnitude v in the direction indicated. The region in the figure is in a uniform magnetic field B, parallel to the x-axis and directed toward the right. Which charges experience a force due to B? What is the direction of the force on each charge?

Short answer

Charge experience zero force, but all other charges will experience some force due to the field velocity

Step-by-step solution

Magnetic field and charge

Magnetic field is the vector field which describe the magnetic influence on moving electric field. Now we know that

$F_{mag}=q\left(\overrightarrow{v}\times \overrightarrow{B}\right)$

Now by applying the above equation, and we get the particle velocity and field in the same direction then the field is zero

If not, then the field is perpendicular to both$\overrightarrow{v}$ and$\overrightarrow{B}$

Charge on the other particles

Only the charge C experience zero force and all other experience some force due to field and velocity.

$\overrightarrow{F}q\left(\overrightarrow{v}\times \overrightarrow{B}\right)$, hence

$F_a$is negative in z direction

$F_b$is positive in y direction

$F_c$is zero

$F_d$is negative in the y direction

$F_e$is $45°$to both negative and y and z axis.