Question
Two point charges and are placed 30 cm apart on the x-axis. Find the position on the line joining them where the electric field is zero. (JEE Main 2023 PYQ pattern.)
Solution — Step by Step
Field is zero only on the line outside the smaller charge — never between two opposite charges (the fields add up there) and never beyond the larger charge (the larger field always wins). So the null point is beyond the side.
Let the null point be at distance from the charge, on the side away from . Then it is at distance from the larger charge.
Cross-multiply and take square roots:
So the null point is 30 cm from the charge, or 60 cm from the charge.
Final answer: 30 cm beyond the charge (60 cm from the positive charge)
Why This Works
Outside the negative charge, both field contributions point in opposite directions (the positive pushes outward, the negative pulls back toward itself). Equating magnitudes finds the cancellation point.
The square-root trick — ratio of distances — is the fastest way to solve this family of questions. Memorise it.
Alternative Method
You could write the field expression with signs and solve . Same answer but more bookkeeping with signs.
Common Mistake
Students place the null point between the two charges. Visualise the field directions first: between and , both arrows point from toward , so they add — never cancel. The null is always on the “outside” of the smaller charge.
JEE Main asks “potential = 0” and “field = 0” questions back to back. Don’t confuse them — potential can be zero between opposite charges (closer to the smaller one), but field cannot.