A point charge of 10 C is placed at the origin. At what location on the X-axis should a point charge of 40 C be placed so that the net electric field is zero at cm on the X-axis?
- A.cm
- B.cm
- C.cm
- D.cm
Show answer and solution
Correct option: C
Solution
At x = 2 cm, the 10 μC charge at the origin produces a field pointing in the +x direction. For the net field to be zero, the 40 μC charge must be placed to the RIGHT of x = 2 cm (so its field points in the −x direction at that point).
Let the 40 μC charge be at x = d. The condition is:
k·10/(0.02)² = k·40/(d − 0.02)²
(d − 0.02)²/(0.02)² = 40/10 = 4
(d − 0.02)/0.02 = 2
d − 0.02 = 0.04 m → d = 0.06 m = 6 cm
The 40 μC charge must be placed at x = 6 cm.
Let the 40 μC charge be at x = d. The condition is:
k·10/(0.02)² = k·40/(d − 0.02)²
(d − 0.02)²/(0.02)² = 40/10 = 4
(d − 0.02)/0.02 = 2
d − 0.02 = 0.04 m → d = 0.06 m = 6 cm
The 40 μC charge must be placed at x = 6 cm.
[JEE Main 2023 · 25 Jan · Shift 2]