Question

1.
Depict the trajectory of a positively charged particle moving with velocity v as
it enters a uniform magnetic field perpendicular to the direction of its propagation. ​

Answer 1

TRAJECTORY OF CHARGE:

• Let's assume that : $\vec{v}=v(\hat{i})$

• And the magnetic field intensity is perpendicular to velocity vector as follows: $\vec{B}=B(-\hat{k})$

So, the initial force experienced by the charge will be in the direction:

$= \hat{i} \times ( - \hat{k}) = \hat{j}$

So, we can see that force is perpendicular upwards (in Y axis) to velocity vector.

• Hence, the charge will move in an arc, because it's getting a centripetal magnetic force.

FINALLY, IT WILL FOLLOW THE CIRCULAR TRAJECTORY !

• See the diagram: At point A , charge enters magnetic field, and starts to experience the magnetic force which acts as the centripetal force and makes an arc until it leaves the magnetic field at point C.

Hope It Helps.