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Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Electric Field and Potential

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Electric Field and Potential

Two particles A and B , possessing opposite charges of +2.0 × 10^...

Two particles

A

and

B

, possessing opposite charges of

+2.0 \times 10^{-6} \text{ C}

and

-2.0 \times 10^{-6} \text{ C}

, are positioned at a separation of

1.0 \text{ cm}

. Determine the electric field at a point located on the axis of the dipole,

1.0 \text{ m}

away from the centre.

Options

A $90 \text{ N C}^{-1}$
B $720 \text{ N C}^{-1}$
C $180 \text{ N C}^{-1}$
D $360 \text{ N C}^{-1}$

Correct answer

D. $360 \text{ N C}^{-1}$

Step-by-step solution

The dipole moment

p

is given by

p = q \times 2a

Substituting the given values:

p = 2.0 \times 10^{-6} \times 1.0 \times 10^{-2} = 2.0 \times 10^{-8} \text{ C m}

The electric field on the axis of a short dipole (

r \gg a

) is given by:

E = \dfrac{1}{4\pi \epsilon_0} \dfrac{2p}{r^3}

Substituting the known values (

r = 1.0 \text{ m}

and

\dfrac{1}{4\pi \epsilon_0} = 9 \times 10^9 \text{ N m}^2 \text{ C}^{-2}

):

E = \dfrac{9 \times 10^9 \times 2 \times 2.0 \times 10^{-8}}{(1.0)^3}

E = 36 \times 10 = 360 \text{ N C}^{-1}

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