Question

A test charge q is located 1 meter from a much larger and stationary charge Q. While at this location, the test charge q, experiences a force of F from the stationary charge Q. The test charge is then moved to a new location 2 meters from Q. What force will the test charge q experience from the stationary charge Q at the new location?

• A. (1/4) F
• B. 1/2 F
• C. F
• D. 2F

Answer 1

The correct option is A (1/4) F

Given : $r_i=1$ m $r_f=2$ m

Initial electric force on the test charge $F=\frac{kQq}{r_i^2}=\frac{kQq}{1^2}=kQq$

Final electric force on the test charge $F^{\prime }=\frac{kQq}{r_f^2}=\frac{kQq}{2^2}=\frac{F}{4}$