Two charges 5 × 10-8 C and -3 × 10-8 C are located 16 cm apart. At w

1.	Two charges 5 × 10-8 C and -3 × 10-8 C are located 16 cm apart. At what point on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
Answer» Given q₁ = 5 × 10^-8 C, r = 16 cm = 0.16 m q₂ = -3 × 10^-8 C Let potential be zero at a distance × metre from positive charge q₁ . ∴ r₁ = x meter r₂ = (0.16 – x) metre S0 V = \(\frac{1}{4\pi\varepsilon_0}\) \(\Big[\frac{q_1}{r_1}+\frac{q_2}{r_2}\Big]\) or = 9 x 10⁹ \(\Big[\frac{5\times10^8}{x}-\frac{3\times10^{-8}}{0.16-x}\Big]\) or \(\frac{5\times10^{-8}}{x}=\frac{3\times10^{-8}}{0.16-x}\) or 0.8 – 5x = 3x or x = 0.1 m = 10 cm.

Two charges 5 × 10-8 C and -3 × 10-8 C are located 16 cm apart. At what point on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

Answer»

Given q₁ = 5 × 10^-8 C, r = 16 cm = 0.16 m q₂ = -3 × 10^-8 C Let potential be zero at a distance × metre from positive charge q₁ .

∴ r₁ = x meter

r₂ = (0.16 – x) metre

S0 V = \(\frac{1}{4\pi\varepsilon_0}\) \(\Big[\frac{q_1}{r_1}+\frac{q_2}{r_2}\Big]\)

or = 9 x 10⁹ \(\Big[\frac{5\times10^8}{x}-\frac{3\times10^{-8}}{0.16-x}\Big]\)

or \(\frac{5\times10^{-8}}{x}=\frac{3\times10^{-8}}{0.16-x}\)

or 0.8 – 5x = 3x

or x = 0.1 m = 10 cm.