Two point charges, q1 and q2, are placed a distance r apart. The electric field is zero at a point P between the charges on the line segment connecting them. We conclude that:

the answer is
q1 and q2 have the same signs but different magnitudes.

any idea as to why this is?

Question

Two point charges, q1 and q2, are placed a distance r apart. The electric field is zero at a point P between the charges on the line segment connecting them. We conclude that:

the answer is
q1 and q2 have the same signs but different magnitudes.

any idea as to why this is?

ookawaiioo · Answer

like charges repel

anonymous · Answer

For any point $x$ away from charge $q_1$ along the line connecting it to $q_2$ we can determine the contributions of both electric fields $E_1,E_2$ from $q_1,q_2$ as follows:
$$E_1\propto{q_1}/x^2\E_2\propto q_2/(r-x)^2$$The point is that the electric field at some point in between is merely the sum of the contributions from the original electric fields (this is called superposition):$$E=E_1+E_2$$Now, for the electric field to be zero at some point, it follows that $E=0$ so in other words $E_1,E_2$ must cancel out. Since the denominators of both are guaranteed to be positive ($x^2,(r-x)^2>0$) it follows that the only way for them to cancel is for $q_1,q_2$ to have opposite sign -- one must be positive and the other must be negative.