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Motion of electron in Electric and Magnetic Fields

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“Both magnetic and electric feilds are perpendicular in a region.If we place an electron at rest in that region.what will be the path followed by that electron ?”

– asked Vimal

When the electron is at rest, it is not affected by magnetic field, but due to electric field, it will begin to move in a direction opposite to the field. This initial direction determines the plane of motion. Then it is acted upon by magnetic field as the motion starts

(The answer is incomplete. I am leaving it for the visitors to think and respond)

Charge is placed at rest in crossed electric and magnetic fields
Let electric and magnetic fields are aligned along z and x directions and charge is placed at the origin of coordinate system. Initially, there is no magnetic force as charge is at rest.
However, there is electric force, which accelerates the charge in z-direction. As the particle acquires velocity in z-direction, the magnetic force comes into play and tries to rotate the particle in xz plane about a center on x-axis.
However, z-component of velocity keeps increasing with time due to electric force in that direction. The magnetic force though draws the charged particle away from z-axis along a curved path. This action of magnetic force is countered by electric force in z-direction. The velocity of charged particle ultimately reduces to zero at x-axis. This cycle repeats itself forming cycloid motion. The cycloid path is generated by a point on the circumference of a
rolling wheel.


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