Question

Two point charges of unknown magnitude and sign are placed a distance d apart. (a) If it is possible to have E = 0 at any point not between the charges but on the line joining them, what are the necessary conditions and where is the point located? (b) Is it possible, for any arrangement of two point charges, to find two points (neither at infinity) at which E = O; if so, under what conditions?​

Answer 1

Explanation:

First keep in mind that when is electric field zero “between” the two charges of non-zero magnitude?

Net electric field intensity E due to fields of two charges of intensities E1 and E2 is zero only when the electric field intensities ([E1]=[E2]) cancel each other out due to same magnitudes and opposite directions there. That point is called neutral zone (or zero field spot.Study at: )

Studying this and observing the above figure I’ve uploaded,you might understand that when there are like charges(having same sign of charges),they “cancel” each other’s field at a point between them.Why?because their fields become equal and oppositely directed at that particular point.That becomes a sort of equipotential surface where there is no potential difference.

Any test charge placed at zero field spot wouldn’t feel any force (of attraction or repulsion).We get a static equilibrium.

Another problem:Where does the zero field spot exists?

For this you can understand that if the two charges with same sign but unequal magnitude are some distance apart,the zero field spot would be nearer to the weak charge (i.e.)charge with smaller magnitude.That is because at larger distance from strong charge (larger magnitude),its field would be fairly weaker and at smaller distance from weak charge(to the same point) would be stronger(talking of weak charge) so that it “equializes” the weaker region of the strong charge.

Or if the concerned charges are with same sign and equal magnitude,the zero field spot would exist in the exact middle of the separating distance of charges.

Conclusion:

The concerned charges are with the same sign.

And;

Zero field spot can exist in middle of the separating distance (if the concerned charges are with same magnitude) or nearer to the weak charge (in case of unequal magnitude)