Derive an expression for the electric field at any point on the equatorial line of an electric dipole.

Consider an electric dipole consisting of charges - q and + q separated by a distance 2 a . Let E A be the electric field at point Q due to charge - q and E B be the electric field at point Q due to charge + q where Q is a point on the equatorial line of the dipole whose electric field is to be measured. Let x be the distance between the centre of the dipole and point Q . Now, resultant electric field at point Q would be, E Q = E A + E B E A = 1 4 π ε 0 q A Q 2 ⇒ 1 4 π ε 0 q x 2 + a 2 ( ∵ According to Pythagoras, A Q = x 2 + a 2 2 ) E B = 1 4 π ε 0 q B Q 2 ⇒ 1 4 π ε 0 q x 2 + a 2 ( ∵ According to Pythagoras, B P = x 2 + a 2 2 ) Now, according to parallelogram law of vector addition, the resultant electric field would become, E Q = E A 2 + E B 2 + 2 E A E B cos 2 θ Now, since E A = E B we can say, E A = E B = E ' E Q = E ' 2 + E ' 2 + 2 E ' E ' cos 2 θ ⇒ 2 E ' 2 ( 1 + cos 2 θ ) ⇒ E ' 2 ( 1 + cos 2 θ ) ⇒ E ' 2 2 cos 2 θ E Q = 2 E ' cos θ - - - ( i ) Now, from △ A O Q , cos θ = a x 2 + a 2 Also, we know that, E ' = 1 4 π ε 0 q x 2 + a 2 Putting both these values in equation ( i ) , we get, E Q = 2 4 π ε 0 q x 2 + a 2 a x 2 + a 2 E Q = p 4 π ε 0 x 2 + a 2 3 2 Since we know that in dipoles, x > > > 2 a , then a 2 can be neglected. ∴ E = p 4 π ε 0 x 3 2

EASY

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What happens to the force between two charges if the distance between them is doubled?

Important Questions on Electric Charges and Fields

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IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 4

A shower of protons from outer space deposits equal

+ q

charge on the earth and the moon and the electrostatic repulsion then exactly counterbalances the gravitational attraction. How large is

q

HARD

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IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 5

Two fixed point charge

+ 4 e

and

+ e

are separated by a distance

' a'

. Where should the third point charge be placed for it to be in equilibrium.

EASY

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IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 6

Define dielectric constant. What do you mean by the statement - dielectric constant of mica is $6$ ?

The mutual force of repulsion between two point charge having fixed distance between them is $9$ Dyne in vacuum and $4$ Dyne in a dielectric medium. What is the dielectric constant of the medium.

MEDIUM

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 7

A sphere of metal has a radius of $12 cm$ and carries a charge of $1.6 \times 10^{- 7} C$ , distributed uniformly on its surface. Calculate the electric field intensity at a point just outside the sphere.

MEDIUM

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 8

Electric field lines are pictorial representation of electric field around a charge, Using Gauss's Law in electrostatics, derive an expression for the electric field due to an uniformly charges thin spherical shell at a point inside the shell.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 9

Write the expression for Electric intensity due to infinite long charged wire at a radial distance

r

from the wire.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 10

A point charge of

2.0 μC

is at the center of a cubic Gaussian surface

9.0 cm

on edge. What is the net electric flux through the surface? (

\in_{0} = 8.854 \times 10^{- 12}

)

EASY

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IMPORTANT

Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 11

If the radius of the gaussian surface enclosing a charge is halved, how does the electric flux through the gaussian surface change?

What happens to the force between two charges if the distance between them is doubled?

Important Questions on Electric Charges and Fields

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