Back to Directory
NEET PHYSICSEasy

A short electric dipole has a dipole moment of 16×109 C m16 \times 10^{-9} \text{ C m}. The electric potential due to the dipole at a point at a distance of 0.6 m0.6 \text{ m} from the centre of the dipole situated on a line making an angle of 6060^{\circ} with the dipole axis is: (14πϵ0=9×109 N m2/C2)(\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ N m}^2/\text{C}^2)

A

200 V200 \text{ V}

B

400 V400 \text{ V}

C

zero

D

50 V50 \text{ V}

Step-by-Step Solution

The electric potential VV due to a short electric dipole at a distance rr from the centre and at an angle θ\theta with the dipole axis is given by the formula: V=14πϵ0pcosθr2V = \frac{1}{4\pi\epsilon_0} \frac{p \cos\theta}{r^2} [NCERT Class 12, Physics Part I, Sec 2.4, Eq 2.15]

  1. Given Data: Dipole moment, p=16×109 C mp = 16 \times 10^{-9} \text{ C m} Distance, r=0.6 mr = 0.6 \text{ m} Angle, θ=60\theta = 60^{\circ} Coulomb constant, k=9×109 N m2C2k = 9 \times 10^9 \text{ N m}^2\text{C}^{-2}

  2. Calculation: Substitute the values into the formula: V=(9×109)×(16×109)×cos(60)(0.6)2V = \frac{(9 \times 10^9) \times (16 \times 10^{-9}) \times \cos(60^{\circ})}{(0.6)^2} Simplify the expression (note 109×109=110^9 \times 10^{-9} = 1 and cos60=0.5\cos 60^{\circ} = 0.5): V=9×16×0.50.36V = \frac{9 \times 16 \times 0.5}{0.36} V=144×0.50.36=720.36V = \frac{144 \times 0.5}{0.36} = \frac{72}{0.36} V=720036=200 VV = \frac{7200}{36} = 200 \text{ V}

Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started