Two small charged spheres A and B have charges 10 μ C and 40 μ C respectively and are held at separation of 90 cm from each other. At what distance from A, electric field intensity would be zero?

Question

Two small charged spheres A and B have charges 10 μ C and 40 μ C respectively and are held at separation of 90 cm from each other. At what distance from A, electric field intensity would be zero? (A) 22.5 cm (B) 18 cm (C) 30 cm (D) 36 cm

Tardigrade Admin · Accepted Answer

Given situation is shown in the figure. Suppose electric field intensity at point C is zero.
Here,

A B = r = 90 c m = 0.9 m

q_{A} = 10 μ C = 10 \times 1 0^{- 6} C

q_{B} = 40 μ C = 40 \times 1 0^{- 6} C, A C = ?

At point

C, E_{A} = E_{B}

\frac{q _{A}}{4 π ε _{0} ( A C ) ^{2}} = \frac{q _{B}}{4 π ε _{0} ( BC ) ^{2}}

\frac{q _{A}}{( A C ) ^{2}} = \frac{q _{B}}{( r - A C ) ^{2}}

\frac{10 \times 1 0 ^{- 6}}{( A C ) ^{2}} = \frac{40 \times 1 0 ^{- 6}}{( 0.9 - A C ) ^{2}}

\frac{1}{( A C ) ^{2}} = \frac{4}{( 0.9 - A C ) ^{2}}; \frac{1}{A C} = \frac{2}{( 0.9 - A C )}

0.9 - . A C = 2 A C; 3 A C = 0.9

A C = 0.3 m = 30 c m

Q. Two small charged spheres A and B have charges 10μC and 40μC respectively and are held at separation of 90cm from each other. At what distance from A, electric field intensity would be zero?

22.5 cm

18 cm

30 cm

36 cm

Q. Two small charged spheres $A$ and $B$ have charges $10 μ C$ and $40 μ C$ respectively and are held at separation of $90 c m$ from each other. At what distance from $A$ , electric field intensity would be zero?