2 points charges +2microC and +8microC are placed 1 meter apart.Find point on the line joining them where the resultant field is 0.

Question

 electric charge 

Answer 1

Let P be the desired point. If P is at a distance x away from the 2 muC charge, then P is at a distance 1 - x away from the 8 muC charge. The electric fields at P due to the two charges face opposite directions, so the resultant field is zero if, and only if, the electric fields at P have equal magnitudes. The magnitude of the field due to the 2 microC charge is k(2 muC)/x^2; the magnitude of the field due to the other charge is k(8 muC)/(1 - x)^2. So 

 

k(2 muC)/x^2 = k(8 muC)/(1 - x)^2

 

Cancel the k on both sides, then rearrange the equation to get

 

(1 - x)^2/x^2 = 4

 

Take the square root on both sides, then cross multiply to obtain

 

1 - x = 2x

 

Then 1 = 3x, or x = 1/3. Hence, the point P is a third of a meter away from the 2 muC charge and two-thirds of a meter away from the 8 muC charge.