Question

Consider an electric dipole of q = 3.0 × 10–6 C and 2l = 4 × 10–10 m. Calculate
the magnitude of dipole moment. Calculate electric field at a point r = 6 × 10–6 m
on the equatorial plane.

Answer 1

magnitude of dipole moment, P = q(2l)

= 3 × 10^-6 C × 4 × 10^-10 m

= 12 × 10^-16 Cm

= 1.2 × 10^-15 Cm

electric field at point , r = 6 × 10^-6 m on the equatorial plane is given as, E = kP/(r² + l²)^(3/2)

here we have , l = 2 × 10^-10 m and r = 6 × 10^-6 = 60000 × 10^-10 m

we see, 2 << 60000

so, l < < r and hence, l² << r²

then, (r² + l²) ≈ r²

now, E = kP/(r²)^(3/2) = kP/r³

= (9 × 10^9 × 1.2 × 10^-15)/(6 × 10^-6)³

= 10.8 × 10^-6/(216 × 10^-18)

= 10.8/216 × 10¹²

= 0.05 × 10¹²

= 5 × 10^10 N/C