What is the force between two small charged sphere having charges of 2 × 10 - 7 C and 3 × 10 - 7 C placed 30 cm apart in air? ( k = 9 × 10 9 Nm 2 C - 2 )

Given, Charge on the first sphere, q 1 = 2 × 10 - 7 C Charge on the second sphere, q 2 = 3 × 10 - 7 C Distance between the spheres is, r = 30 c m = 0.3 m The proportionality constant, k = 9 × 10 9 Nm 2 C - 2 Now, from the coulomb's law, force F = k q 1 q 2 r 2 = 9 × 10 9 × 2 × 10 - 7 × 3 × 10 - 7 ( 0 .3 ) 2 = 6 × 10 - 3 N

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

Derive an expression for the intensity of the electric field at a point on the axial line of an electric dipole.

Consider an electric dipole consisting of charges - q and + q which are separated by a distance of 2 a with a point O being the centre. Let a point P be at the axial line of dipole whose electric field is to be calculated. Let r be the distance between P and O . Let E A be the electric field due to charge - q and E B be the electric field due to charge + q . E A = 1 4 π ε 0 q A P 2 ⇒ 1 4 π ε 0 q a + r 2 E B = 1 4 π ε 0 q B P 2 ⇒ 1 4 π ε 0 q r - a 2 Since E A and E B are opposite to each other and E B > E A , then the resultant intensity at P would be, E = E B - E A ⇒ 1 4 π ε 0 q r - a 2 - 1 4 π ε 0 q r + a 2 ⇒ q 4 π ε 0 1 r - a 2 - 1 r + a 2 ⇒ q 4 π ε 0 r + a 2 - r - a 2 r 2 - a 2 2 ⇒ q 4 π ε 0 4 r a r 2 - a 2 2 ⇒ q 4 π ε 0 2 a 2 r r 2 - a 2 2 ⇒ 1 4 π ε 0 2 p r r 2 - a 2 2 Also, if r > > > a , then, E = 1 4 π ε 0 2 p r 3 .

State Gauss Law of electrostatics and explain it's importance.

Gauss's law states that total electric flux through any closed surface is equal to 1 ∈ 0 times the net charge enclosed by the surface. Total flux ϕ = ∮ E . → d s → = q ∈ 0 Importance : (1) Gauss's law is very useful in calculating the electric field in case of problems where it is possible to construct a closed surface by making a Gaussian surface. (2) Gauss's law is true for any closed surface, no matter what its shape or size. (3) Symmetric considerations in many problems make the application of Gauss's law much easier.

HARD

12th Andhra Pradesh Board

IMPORTANT

Earn 100

Two infinitely long thin straight wires having uniform linear charge densities $λ$ and $2 λ$ are arranged parallel to each other at a distance $r$ apart. Calculate intensity of the electric field at a point midway between them.

Important Questions on Electric Charges and Fields

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 4 - Electric Charges and Fields>MODEL QUESTIONS (IPE PATTERN)>Q 10

Two infinitely long thin straight wires having uniform linear charge densities

e

and

2 e

are arranged parallel to each other at a distance

r

apart. Calculate intensity of the electric field at a point midway between them.

HARD

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 4 - Electric Charges and Fields>MODEL QUESTIONS (IPE PATTERN)>Q 11

An electron of mass $m$ and charge $e$ is fired perpendicular to a uniform electric field of intensity $E$ with an initial velocity $u$ . If the electron traverses a distance $x$ in the field in the direction of firing, find the transverse displacement $y$ it suffers.

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 4 - Electric Charges and Fields>MODEL QUESTIONS (IPE PATTERN)>Q 4.1

What is the force between two small charged sphere having charges of

2 \times 10^{- 7} C

and

3 \times 10^{- 7} C

placed

30 cm

apart in air? (

k = 9 \times 10^{9} {Nm}^{2} C^{- 2}

)

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 4 - Electric Charges and Fields>MODEL QUESTIONS (IPE PATTERN)>Q 4.2

The electrostatic force on a small sphere of charge

0.4 µ C

due to another small sphere of charge

- 0.8 µ C

in the air is

0.2 N .

What is the distance between the two spheres? (

k = 9 \times 10^{9} {Nm}^{2} C^{- 2}

)

EASY

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 4 - Electric Charges and Fields>MODEL QUESTIONS (IPE PATTERN)>Q 4.2

The electrostatic force on a small sphere of charge

0.4 µ C

due to another small sphere of charge

- 0.8 µ C

in the air is

0.2 N .

What is the force on the second sphere due to the first?

MEDIUM

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 4 - Electric Charges and Fields>MODEL QUESTIONS (IPE PATTERN)>Q 4.3

Check that the ratio

k e^{2} / G m_{e} m_{p}

is dimensionless. Look up a table of physical constants and determine the value of this ratio. What does the ratio signify?

EASY

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 4 - Electric Charges and Fields>MODEL QUESTIONS (IPE PATTERN)>Q 4.4

Explain the meaning of the statement ‘electric charge of a body is quantized’.

EASY

12th Andhra Pradesh Board

IMPORTANT

Intermediate Second Year Physics>Chapter 4 - Electric Charges and Fields>MODEL QUESTIONS (IPE PATTERN)>Q 4.4

Why can one ignore the quantization of electric charge when dealing with macroscopic i.e., large-scale charges?

Two infinitely long thin straight wires having uniform linear charge densities λ and 2λ are arranged parallel to each other at a distance r apart. Calculate intensity of the electric field at a point midway between them.

Important Questions on Electric Charges and Fields

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Two infinitely long thin straight wires having uniform linear charge densities $λ$ and $2 λ$ are arranged parallel to each other at a distance $r$ apart. Calculate intensity of the electric field at a point midway between them.