A uniformly charged sphere carries a total charge 2 π × 10 − 12 C . Its radius is 5 cm and is placed in vacuum. Determine its surface charge density.

Given, Total charge q = 2 π × 10 − 12 C Radius r = 5 cm = 5 × 10 − 2 m The surface charge density formula is given by, σ = q A Where, σ is surface charge density, q is charge, A is surface area ∴ σ = q 4 πr 2 = 2 π × 10 − 12 4 π 5 × 10 − 2 2 = 2 × 10 − 10 C m − 2

A uniformly charged sphere carries a total charge 2 π × 10 − 12 C . Its radius is 5 cm and is placed in vacuum. Determine its surface charge density.

Given, Total charge q = 2 π × 10 − 12 C Radius r = 5 cm = 5 × 10 − 2 m The surface charge density formula is given by, σ = q A Where, σ is surface charge density, q is charge, A is surface area ∴ σ = q 4 πr 2 = 2 π × 10 − 12 4 π 5 × 10 − 2 2 = 2 × 10 − 10 C m − 2

A dipole consisting of an electron and a proton separated by a distance of 4 × 10 − 10 m is situated in an electric field of intensity 3 × 10 5 NC − 1 at an angle of 30 o with the field. Calculate the dipole moment and the torque acting on it. Charge on an electron = 1 .602 × 10 − 19 C .

Given, Magnitude of each charge of the dipole q = e = 1 .602 × 10 − 19 C Separation between charges d = 4 × 10 − 10 m Intensity of the electric field E = 3 × 10 5 NC − 1 Angle between the electric field and the dipole moment θ = 30 ∘ Magnetic dipole moment p = q × d = 1 .602 × 10 − 19 × 4 × 10 − 10 ≃ 6 .41 × 10 − 29 Cm Torque on the dipole τ = pEsin θ = 6 .41 × 10 − 29 × 3 × 10 5 × sin 30 ∘ Torque on the dipole = 6 .41 × 10 − 29 × 3 × 10 5 × 1 2 So the torque on the dipole = 9 .615 × 10 − 24 Nm

An electric dipole is placed at an angle of 60 o with an electric field of magnitude 4 × 10 5 NC − 1 . It experiences a torque of 8 3 Nm . If the length of the dipole is 4 cm , determine the magnitude of either charge of the dipole.

Given, Torque on the dipole τ = 8 3 Nm Magnitude of the field strength E = 4 × 10 5 NC − 1 Length of the dipole d = 4 cm = 4 × 10 − 2 m Angle between the electric field and the dipole moment θ = 60 ∘ Torque on the dipole τ = pE sin θ = qdE sin θ ⇒ q = τ dE sin θ = 8 3 0 .04 × 4 × 10 5 × sin 60 ∘ = 8 3 0 .04 × 4 × 10 5 × 3 2 = 10 − 3 C Magnitude of the either charge of the dipole q = 10 − 3 C

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12th CBSE

IMPORTANT

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A uniformly charged sphere carries a total charge $2 π \times 10^{- 12} C$ . Its radius is $5 cm$ and is placed in vacuum. Determine its surface charge density.

Important Questions on Electric Charges and Field

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 2

What charge would be required to electrify a sphere of radius

15 cm

so as to get a surface charge density of

\frac{7}{11} μ C m^{- 2}

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 3

A metal cube of length

0.1 m

is charged by

12 μC

. Calculate its surface charge density.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 4

Two equal spheres of water having equal and similar charges coalesce to form a large sphere. If no charge is lost, how will the surface densities of electrification change?

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12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 1

An electric dipole is formed by

+ 4 μC

and

- 4 μC

charges at

5 mm

distance. Calculate the dipole moment and give its direction.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 2

An electric dipole of dipole moment

4 \times 10^{- 5} Cm

is placed in a uniform electric field of

10^{- 3} {NC}^{- 1}

making an angle of

30^{o}

with the direction of the field. Determine the torque exerted by the electric field on the dipole.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 3

A dipole consisting of an electron and a proton separated by a distance of

4 \times 10^{- 10} m

is situated in an electric field of intensity

3 \times 10^{5} {NC}^{- 1}

at an angle of

30^{o}

with the field. Calculate the dipole moment and the torque acting on it. Charge on an electron

= 1 .602 \times 10^{- 19} C

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 4

An electric dipole is placed at an angle of

60^{o}

with an electric field of magnitude

4 \times 10^{5} {NC}^{- 1}

. It experiences a torque of

8 \sqrt{3} Nm

. If the length of the dipole is

4 cm

, determine the magnitude of either charge of the dipole.

EASY

12th CBSE

IMPORTANT

New Simplified Physics (Vol 1) For Class 12>Chapter 1 - Electric Charges and Field>Problems For Practice>Q 5

An electric dipole consists of two opposite charges of magnitude

2 \times 10^{- 6} C

each and separated by a distance of

3 cm

. It is placed in an electric field of

2 \times 10^{5} {NC}^{- 1}

. Determine the maximum torque on the dipole.

A uniformly charged sphere carries a total charge 2π×10−12C. Its radius is 5 cm and is placed in vacuum. Determine its surface charge density.

Important Questions on Electric Charges and Field

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A uniformly charged sphere carries a total charge $2 π \times 10^{- 12} C$ . Its radius is $5 cm$ and is placed in vacuum. Determine its surface charge density.