A point charge of 5 × 10 - 6 C experiences a force of 2 × 10 - 3 N when kept in a uniform electric field of intensity E . Find E .

Given that charge = q = 5 × 10 - 6 C and experienced force = F = 2 × 10 3 N According to relation between electrostatic force and electric field intensity F = qE ⇒ E = F q = 2 × 10 - 3 5 × 10 - 6 = 2 × 10 3 5 = 400 NC - 1

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

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When is the electric flux negative and when is it positive?

Important Questions on Electric Charges and Fields

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 19

Consider a uniform electric field

E = 3 \times 10^{3} N / C

. What is the flux of this field through a square of

10 cm

on a side whose plane is parallel to the

y z

plane?

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 20

What is electric flux? What is its unit? What is electric flux density?

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 21

An electric dipole having dipole moment $4 \times 10^{- 9} C m$ is oriented at $30^{°}$ from the direction of a uniform electric field of magnitude $5 \times 10^{4} {NC}^{- 1}$ . Calculate the magnitude of the torque on the dipole.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 22

A point charge of

5 \times 10^{- 6} C

experiences a force of

2 \times 10^{- 3} N

when kept in a uniform electric field of intensity

E

. Find

E

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 23

A thick chain hangs from a petrol or a diesel tanker and it is in contact with ground when the tanker is moving.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 24

Explain the concept of electric field. Express electric flux through a surface in terms of electric field intensity. Show that the electric flux through a cylindrical surface with its axis parallel to a uniform electric field is zero.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 25

Name the basic properties of electric charge.

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Physics Crash Course (Based on Revised Syllabus-2023)>Chapter 1 - Electric Charges and Fields>Exercise>Q 26

There are four charges, each with a magnitude

Q

. Two are positive and two are negative. The charges are fixed to the corners of a square of side

' L'

, one to each corner, in such a way that the force on any charge is directed toward the center of the square. Find the magnitude of the net electric force experienced by any charge?

When is the electric flux negative and when is it positive?

Important Questions on Electric Charges and Fields

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