Asmall segment of wire contains 10 nc of charge. the segment is shrunk to one-third of its original length. a proton is very far from the wire. what is the ratio ff/fi of the electric force on the proton after the segment is shrunk to the force before the segment was shrunk?

To solve this problem we will apply the concepts related to the electric field, linear charge density and electrostatic force.

The electric field is

Here,

= Linear charge density

= Permittivity of free space

r = Distance

The linear charge density can be written as,

Linear charge density is given as

Replacing,

The initial and final electric Force can be written as function of the charge and the electric field as

If we replace the value for the electric field we have,

Length is one third at the end, then

The ratio of the force is

Therefore the required ratio is 3

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