Question

a short dipole of dipole moment 4 microC-mî is plased at the origin. the electric potential due to thee dipole at the coordinate (3m,4m) in x,y-plane is

Answer 1

magnitude of dipole moment, P = 4uC.m

= 4 × 10^-6 C.m

separation between midpoint of dipole to point of observation, r =√(3-0)² + (4 - 0)² = 5m [ here we assume midpoint of dipole is located at origin.]

angle made by r to dipole axis, θ = tan^-1(4/3) or cos^-1(3/5)

using formula

electrical Potential = KPcosθ/r²

= 9 × 10^9Nm²/C² × 4 × 10^-6C.m × cos(cos^-1(3/5))/(5m)²

= 36 × 10³ × (3/5)/25 volts

= (108/125) × 10³ Volts

= 0.864 × 10³ volts

= 864 volts.

hence, electrical potential due to the dipole at (3, 4) in x-y plane is 864 volts.