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

Question

A ring of diameter 9.00 cm is fixed in place and carries a charge of +5.00 C uniformly spread over its circumference. (a) How much work does it take to move a tiny +3.10- charged ball of mass 1.40 g from very far away to the center of the ring? (Assume the ball is moved along the axis of the ring.) (b) Is it necessary to take a path along the axis of the ring? (L.e is the amount of work done dependent on the path taken to bring the ball to the center of the ring?) Yes No Why? (c) If the bal is slightly displaced from the center of the ring, what will it do? (Assume the displacement is along the axis of the ring.) × accelerate away from the ring accelerate toward the ring What is the maximum speed it will reach? × × × m/s

Explanation / Answer

a)
Potential at the center of the ring, V = k*Q/r

= 9*10^9*5*10^-6/0.045

= 1*10^6 v

potentail energy of the charge, U = q*delta_V

= 3.1*10^-6*1*10^6

= 3.1 J

b) No.

Because electric force is conservative force. so, workdone by electric force does not depend on path.

c) accelerate away from the ring

d) let v is the speed of the charged particle.

initial potential energy = final kinetic energy

U = 0.5*m*v^2

==> v = sqrt(2*U/m)

= sqrt(2*3.1/(1.4*10^-3))

= 66.55 m/s

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