Aproton is acted on by an uniform electric field of magnitude 183 n/c pointing in the positive y-direction. the particle is initially at rest. (a) in what direction will the charge move?
(b) determine the work done by the electric field when the particle has moved through a distance of 4.15 cm from its initial position.
(c) determine the change in electric potential energy of the charged particle.
(d) determine the speed of the charged particle.

Part a)

charge will move initially in +Y direction

Part b)

Part c)

Part d)

Explanation:

Part a)

Since electric field is in +Y direction so positive charge will move in the same direction

So charge will move initially in +Y direction

Part b)

Force due to electric field on the charge is given as

now work done to move it by 4.15 cm is given as

Part c)

As we know that work done by conservative force is negative change in potential energy

so we will have

Part d)

Work done by electric field = change in kinetic energy of the charge particle

here we have

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min