A ring of diameter 9.00 cm is fixed in place and carries a charge of +5.00 A rin

Question

A ring of diameter 9.00 cm is fixed in place and carries a charge of +5.00

A ring of diameter 9.00 cm is fixed in place and carries a charge of +5.00 mu C uniformly spread over its circumference. How much work does it take to move a tiny +2.80- mu C charged ball of mass 1.10 g from very far away to the center of the ring? Is it necessary to take a path along the axis of the ring? (I.e. is the amount of work done dependent on the path taken to bring the ball to the center of the ring?) If the ball is slightly displaced from the center of the ring, what will it do? What is the maximum speed it will reach?

Explanation / Answer

diameter of ring d = 9.00 cm

radius is r = (d/2) = 4.50 cm = 4.50 x 10^-2 m

charge on the ring q = +5.00 uC = +5.00 x 10^-6 C

a)the electric field on the axis of ring is

Ex = (k x s x q/(s^2 + r^2)^3/2)

where k = (1/4pi x e_o) = 9 x 10^9 Nm^2/C^2 and s is distance from center of ring to the point where the charge is located

The force acting on the tiny charge is

F = Ex x q1

where q1 = +2.80 uC = +2.80 x 10^-6 C

the work done on the charge is

W = F x s

b)The amount of work depends on the path taken to bring the charge to the center of ring.This is because the electric field acts only along the axis of the ring and on other side it has zero value.

c)As the charge on the ring and charge on the ball are both positive,therefore the ball will be slightly repeled away from the axis of the ring.

d)let the maximum speed be v

we know that

W = (1/2)mv^2

or v^2 = (2W/m)

or v = (2W/m)^1/2

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