An infinite line charge produces a field of 9 × 10 4 N C at a distance of 2 cm . Calculate the linear charge density. Take, ∈ 0 = 8 . 854 × 10 - 12 C 2 / N . m 2

Given, Distance, d = 2 c m = 0.02 m Electric Field, E = 9 × 10 4 N / C Say, the linear charge density is λ . The formula for electric field produced by infinite line charge is given as, E = λ 2 π ∈ 0 d ⇒ λ = 2 π ∈ 0 d E = 2 × 3 . 14 × 8 . 854 × 10 - 12 × 0 . 02 × 9 × 10 4 = 0 . 1 μC / m

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17 × 10 - 12 C / m 2 . What is E : a) in the outer region of the first plate b) in the outer region of the second plate and c) between the plates? Take, ∈ 0 = 8 .854 × 10 - 12 N - 1 C 2 m - 2 .

A and B are two parallel plates close to each other. Outer region of plate A is labeled as I , outer region of plate B is labeled as I I I , and the region between the plates, A and B , is labeled as I I . Charge density of plate A , σ = 17.0 × 10 - 12 C / m 2 In the regions, I and I I I , electric field E is zero because the fields due to the equal and opposite charges on the plates gets canceled. Electric field E in region I I is, E = σ ∈ 0 = 17 .0 × 10 - 12 8 .854 × 10 - 12 = 1.92 N / C . Therefore, electric field between the plates is 1.92 N / C .

An oil drop of 12 excess electrons is held stationary under a constant electric field of 2 . 55 × 10 4 N / C (Millikan’s oil drop experiment). The density of the oil is 1 . 26 gm cm 3 . Estimate the radius of the drop. ( g = 9 . 8 m / s 2 ; e = 1 . 6 × 10 - 19 C ).

Given, Excess electrons on an oil drop, n = 12 Electric field intensity, E = 2.55 × 10 4 N C - 1 Density of oil, ρ = 1 .26 gm / cm 3 = 1 .26 × 10 3 kg/m 3 Acceleration due to gravity, g = 9.8 m s - 2 Charge on an electron, e = 1.6 × 10 - 19 C The total charge of the drop then becomes, q = n e = 12 × 1 . 6 × 10 - 19 C = 19 . 2 × 10 - 19 C Say, the radius of the sphere is r . The volume of the sphere then becomes, v = 4 3 π r 3 The mass of the sphere becomes, m = v ρ = 4 3 π r 3 ρ As the charge is held stationary under the electric field, the net force on a drop must be zero. Therefore, the force due to the electric field must be equal to the force due to gravity. ⇒ q E = m g ⇒ q E = 4 3 π r 3 ρ r = 3 E q 4 π ρ g 3 = 3 × 2.55 × 10 4 × 19 . 2 × 10 - 19 4 × 3.14 × 1.26 × 10 3 × 9.8 3 = 946.09 × 10 - 21 3 = 9.82 × 10 - 7 m

MEDIUM

12th Madhya Pradesh Board

IMPORTANT

Earn 100

A point charge $+ 10 μC$ is a distance $5 cm$ directly above the centre of a square of side $10 cm$ , as shown in the figure. What is the magnitude of the electric flux through the square? (Take, $\in_{0} = 8.854 \times 10^{- 12} C$ )

Important Questions on Electric Charges and Fields

EASY

12th Madhya Pradesh Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>EXERCISES>Q 1.19

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

12th Madhya Pradesh Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>EXERCISES>Q 1.2

A point charge causes an electric flux of

- 1.0 \times 10^{3} \frac{{Nm}^{2}}{C}

to pass through a spherical Gaussian surface of

10 cm

radius centered on the charge.
If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?

MEDIUM

12th Madhya Pradesh Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>EXERCISES>Q 1.2

A point charge causes an electric flux of

- 1.0 \times 10^{3} {Nm}^{2} C^{- 1}

to pass through a spherical Gaussian surface of

10 cm

radius centered on the charge. What is the value of the point charge? (

\in_{0} = 8.854 \times 10^{- 12} N^{- 1} m^{- 2} C^{2}

)

MEDIUM

12th Madhya Pradesh Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>EXERCISES>Q 1.21

A conducting sphere of radius

10 cm

has an unknown charge. If the electric field

20 cm

from the center of the sphere is

1.5 \times 10^{3} \frac{N}{C}

and points radially inward, what is the net charge on the sphere?

MEDIUM

12th Madhya Pradesh Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>EXERCISES>Q 1.22

A uniformly charged conducting sphere of

2.4 m

diameter has a surface charge density of

80 μC / m^{2}

. Find the charge on the sphere. What is the total electric flux leaving the surface of the sphere?

MEDIUM

12th Madhya Pradesh Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>EXERCISES>Q 1.23

An infinite line charge produces a field of

9 \times 10^{4} \frac{N}{C}

at a distance of

2 cm

. Calculate the linear charge density. Take,

\in_{0} = 8.854 \times 10^{- 12} C^{2} / N . m^{2}

MEDIUM

12th Madhya Pradesh Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>EXERCISES>Q 1.24

Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude $17 \times 10^{- 12} C / m^{2}$ . What is $E$ : a) in the outer region of the first plate b) in the outer region of the second plate and c) between the plates? Take, $\in_{0} = 8 .854 \times 10^{- 12} N^{- 1} C^{2} m^{- 2}$ .

HARD

12th Madhya Pradesh Board

IMPORTANT

PHYSICS PART-1 TEXTBOOK FOR CLASS XII>Chapter 1 - Electric Charges and Fields>ADDITIONAL EXERCISES>Q 1.25

An oil drop of

12

excess electrons is held stationary under a constant electric field of

2.55 \times 10^{4} N / C

(Millikan’s oil drop experiment). The density of the oil is

1.26 \frac{gm}{{cm}^{3}}

. Estimate the radius of the drop. (

g = 9.8 m / s^{2}

;

e = 1.6 \times 10^{- 19} C

A point charge +10 μC is a distance 5 cm directly above the centre of a square of side 10 cm, as shown in the figure. What is the magnitude of the electric flux through the square? (Take, ∈0 = 8.854×10-12 C)

Important Questions on Electric Charges and Fields

Learn and Prepare for any exam you want !

A point charge $+ 10 μC$ is a distance $5 cm$ directly above the centre of a square of side $10 cm$ , as shown in the figure. What is the magnitude of the electric flux through the square? (Take, $\in_{0} = 8.854 \times 10^{- 12} C$ )