electric field

Question

Two point charges +q and -4q are placed at x=0 and x=L respectively. At what point on the x-axis is the electric field zero?

RankGuru · Accepted Answer

1. **Identify the smaller charge**: The null point (where the electric field is zero) occurs where the fields from the two charges cancel out. This is closer to the smaller magnitude charge ($+q$) and located outside the region between the charges because they have opposite signs.
2. **Set up the Equation**: Let the point be at a distance $d$ from $+q$ on the left side (x-axis). The condition for zero electric field is:
   $$k \frac{q}{d^2} = k \frac{4q}{(L + d)^2}$$
3. **Solve for d**: Taking the square root of both sides:
   $$\frac{1}{d} = \frac{2}{L + d} \implies L + d = 2d \implies d = L$$
4. **Find the Coordinate**: Since the point is distance $L$ to the left of $x=0$, the coordinate is $x = -L$.

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