Two charges of 4 μC and 16 μC are separated by a distance of 30 cm. Calculate the distance of the point from the smaller charge where the electric field intensity between them will be zero

r = 0.1 m = 10 cm

Explanation:

To find the position in which the magnitude of the electric field is zero you use the following formula for E:

you can formulate the total electric field of both charges in the following way:

But ET = 0 for r, the you have:

Thus, you have a quadratic equation. You replace the values of the charges and then you use the quadratic formula to get the roots of the polynomial:

when you has taken the positive root because it has physical meaning.

hence, the distance in which ET = 0 is 0.1m = 10cm from the smaller charge