First slide

Force on a charged particle moving in a magnetic field

Question

A charged particle carrying a charge +Q is fixed at point 0, A uniform magnetic field of induction $\vec{B}$ exists in the region which points out of the plane of the page. An electron is projected from point P with velocity $\vec{V}$ as shown in the figure. Then path of the electron

Moderate

A

is a straight line
B

a helix
C

a parabola
D

a circle

Solution

From the diagram it is evident that electric force $F = \frac{1}{4 π \in_{o}} \frac{Qe}{{(OP)}^{2}}$ acting on the electron is radially inward and the magnetic force $\vec{F} = (- e) \vec{V} \times \vec{B}$ is also radially inward. Therefore net force acting on the electron is always radially in ward and always perpendicular to the direction of motion. Hence the path is a circle.

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