A 4.0 micro Coulomb is 3.0 meters away from a 1.0 micro Coulomb charge. There ar

Question

A 4.0 micro Coulomb is 3.0 meters away from a 1.0 micro Coulomb charge. There are no other charges in the area. Where should a third charge (of unknown size) be placed so that the total electrostatic force on that third charge is zero?

A. In between the two charges, 2.0 meters from the 1.0 micro Coulomb charge and thus 1.0 meter away from the 4.0 micro Coulomb charge.

B. There is no location where the total electrostatic force on the third charge can possibly be zero.

C. In between the two charges, 2.0 meters from the 4.0 micro Coulomb charge and thus 1.0 meter away from the 1.0 micro Coulomb charge.

Explanation / Answer

Consider a charge q is placed in between 4.0 micro Coulomb and 1.0 micro Coulomb x meter away from 4.0 micro Coulomb. F acting on q due to 4.0 micro Coulomb = k*q* 4/ (x^2) F acting on q due to 1.0 micro Coulomb = k*q* 1/ (3 -x)^2 Fnet = 0 ( for no electrostatic force on third charge) k*q* 4/ (x^2) - k*q* 1/ (3 -x)^2 = 0 x^2/ (3-x)^2 = 4 x/ 3-x = +/- 2 x = 2 meter or 6 meter x cannot be 6 meter thus option c is correct.

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