Question

Two point charges 2 μC and 8 μC are placed at x = 0 m and x = 3 m on x-axis respectively. The position between the two charges where net electric field is zero is A)x=1 B)x=2 C)x=1.5 D)x=1.25

Answer 1

The position between the two charges where net electric field is zero is x = 1

Therefore, option (B) is correct.

Explanation:

We know that electric field due to a charge q, at a distance is given by

$\boxed{E=k\frac{q}{r^2}}$  (where k is Coulomb's constant)

The given charges are 2 μC and 8 μC and distance between them is 3 m

Let electric field is zero at a distance r from 2 μC charge

Then

$k\frac{2}{r^2}=k\frac{8}{(3-r)^2}$

$\implies \frac{1}{r^2}=\frac{4}{(3-r)^2}$

$\implies (3-r)^2=4r^2$

$\implies r^2-6r+9=4r^2$

$\implies 3r^2+6r-9=0$

$\implies r^2+2r-3=0$

$\implies r^2+3r-r-3=0$

$\implies r(r+3)-1(r+3)=0$

$\implies (r-1)(r+3)=0$

$\implies r=-3,1$

But r cannot be negative

Therefore, r=1

Thus, the position on x -axis where net field is zero is x = 1

Hope this answer is helpful.

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