My notes an electron is released from rest on the axis of a uniform positively charged ring, 0.500 m from the ring's center. if the linear charge density of the ring is +0.100 µc/m and the radius of the ring is 0.700 m, how fast will the electron be moving when it reaches the center of the ring?

Velocity of the electron = v = 1.2\times 10^8\ m/s.

Explanation:

Given,

Now total charge on the ring =

Potential energy due to the charged ring to the point on the x-axis is

Let v be the velocity of the electron at the center of the ring.

Total kinetic energy of the electron =

Now, From the conservation of energy,

the total potential energy of the electron at initially is converted to the total kinetic energy of the electron at the center of the ring,

Hence the velocity of the electron on the center of the charged ring is

it becomes positively charged by charging it

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