The irregularly shaped area of positive charge in the figure below has an initia

Question

The irregularly shaped area of positive charge in the figure below has an initial surface charge density eta_¡. Then the area is shrunken in such a way that it maintains its shape but each dimension (x and y) of the area is reduced by a factor of 3.163. What is the value of the ratio eta_f/eta_i, where eta_f is the final surface charge density? An electron is located very far away from this area of charge. What is the value of the ratio F_f/F_i, where F_f is the electric force on the electron after the area is reduced and F_i is the initial force on the electron before the area was reduced?

Explanation / Answer

(A) surface charge density = charge / area

charge is constant but area is reduced hence charge denisty will increase.

so nf / ni = Ai/ Af = (3.163^2)

nf / ni = 10

(B) as electron is very far away hence this area charge will behave as point charge.

hence force will also be same.

Ff / Fi = 1

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