A ring of diameter 7.00 cm is fixed in place and carries a charge of +5.00 HC un

Question

A ring of diameter 7.00 cm is fixed in place and carries a charge of +5.00 HC uniformly spread over its circumference C charged ball of mass 1.70 g from very far away to a) How much work does it take to move a tiny 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? (I.e. s the amount of work done dependent on the path taken to bring the ball to the center of the ring?) Yes No Why? This answer has not been graded yet. (c) If the ball is slightly displaced from the center of the ring, what will it do? (Assume the displacement is along the axis of the ring.) accelerate toward the ring accelerate away from the ring What is the maximum speed it will reach? m/s

Explanation / Answer

a) radius of the ring, r = d/2 = 7/2 = 3.5 cm = 0.035 m

potential at the center, v = k*Q/r

= 9*10^9*5*10^-6/0.035

= 1.285*10^6 volts

workdone, W = q*delta_V

= 3.2*10^-6*1.285*10^6

= 4.11 J

b) no, workdone does not depend on the path.

because electric force is consrvative force.so, workdone by electric force does not depend on path.

c) accelerate away from the ring.

let v is the speed of the charged particle.

Apply energy conservation.

initial potentail enrgy = final kinetic energy

q*delta_V = 0.5*m*v^2

v = sqrt(2*q*delta_V/m)

= sqrt(2*4.11/(1.7*10^-3))

= 69.5 m/s <<<<<<<--------ANswer

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