At a distance D from a very long (essentially infinite) uniform line of charge, the electric field strength is 1000 N/C. At what distance from the line will the field strength to be 2000 N/C?
A) 2D
B) D
C) D/
D) D/2
E) D/4

Question

At a distance D from a very long (essentially infinite) uniform line of charge, the electric field strength is 1000 N/C. At what distance from the line will the field strength to be 2000 N/C?
A) 2D 
B) D 
C) D/ 
D) D/2 
E) D/4

Quizplus · Accepted Answer

The electric field strength due to a uniformly charged infinite line at a distance D from it is given by E = λ/2πε0D, where λ is the linear charge density of the line and ε0 is the permittivity of free space.

If the electric field strength is doubled to 2000 N/C, then we have 2000 = λ/2πε0x, where x is the new distance from the line. Dividing this equation by the original equation, we get 2 = x/D, or x = 2D.

Therefore, the distance from the line at which the electric field strength is doubled is twice the original distance, which is D/2.

Hence, the answer is D) D/2.

At a Distance D from a Very Long (Essentially Infinite)