Question

two particles a and b having charges 2*10^-6 and of -4*10^-6 held at a separation of 20cm locate the point on the line ab where the electric field and electric potential is zero

Answer 1

charges are opposite in nature so, it can't be possible that electric field zero between them. let r distance from 2 × 10^-6 C , electric field is zero.

so, net electric field at r = 0

or, electric field due to 2 × 10^-6 + electric field due to -4 × 10^-6 = 0

or, k(2 × 10^-6)/r² - k(4 × 10^-6)/(r + 20)² = 0

or, 2 × 10^-6/r² = 4 × 10^-6/(r + 20)²

or, 1/r² = 2/(r + 20)²

or, 1/r = √2/(r + 20)

or, r + 20 = √2r

or, r = 20/(√2 - 1) = 20(√2 + 1) cm from charge 2 × 10^-6 C

electrical potential will be zero between the charges. Let x distance from charge 2 × 10^-6 C electrical potential is zero.

so, k(2 × 10^-6)/x + k(-4 × 10^-6)/(20 - x)=0

or, 2/x = 4/(20 - x)

or, 1/x = 2/(20 - x)

or, 2x = 20 - x

x = 20/3 cm from charge 2 × 10^-6 C