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Electromagnetic Theory I (PH403) Minor Examination: University of Hyderabad - Prof. Biswas, Exams of Electrodynamics

University of Hyderabad Electrodynamics

Prof. Shamal Biswas

these are the questions of both minor and major of 2022 electrostatics classes

Typology: Exams

2021/2022

Uploaded on 04/23/2023

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School of Physics

University of Hyderabad

Minor examination

Electromagnetic Theory – I (PH403)

Date: 15/12/2021 Grade point: 25 Time: 1 hour

--------------------------------------------------------------------------------------------------------

(1-5 , each question contains 1 mark)

1. Find the net force acting on 2q.

a) ) 4𝑘𝑄𝑞𝑧

(𝑧2+𝑑2)3

2𝑘

 (b) 4𝑘𝑄𝑞𝑧

(𝑧2+𝑑2)−3

2𝑘

 (c) 4𝑘𝑄𝑞𝑧

(𝑧2+𝑑2)1

2𝑘

 (d) 4𝑘𝑄𝑞𝑧

(𝑧2+𝑑2)3

2𝑗

2. Two free charges 2q and 5q are placed apart at a distance d. to bring the system

is in equilibrium, the location of the third charge must be at a distance

(a) √2

5 d (b) √2 𝑑

√5− √2 (c) √5 𝑑

√5+ √2 (d) √2 𝑑

2−√5

3. A charge q is placed at the centre of the cube. Then the flux of 𝐸

󰇍

through the

shaded region is

a) 𝑞

48𝜖0 (b) 𝑞

6𝜖0 (c) 𝑞

24𝜖0 (d) 𝑞

12𝜖0

4. The amount of workdone to assemble the whole configuration of four charges is

a) 2𝑘𝑞2

𝑎(1

√2−2) (b) 2𝑘𝑞2

𝑎(1

√2+2)

(c) 𝑘𝑞2

𝑎(1

√2−2) (d) 𝑘𝑞2

𝑎(1

√2+2)

5. Which of the following potentials satisfy the Laplace’s equation?

1. V = 𝑥2−𝑦2+𝑧2 2. V = r cos + z 3. V = rcos + 

(a) 1&2 (b) 1&3 (c) 2&3 (d) 1,2&3

-q

q

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School of Physics University of Hyderabad Minor examination Electromagnetic Theory – I (PH403) Date: 15 / 12 /202 1 Grade point: 25 Time: 1 hour -------------------------------------------------------------------------------------------------------- (1-5 , each question contains 1 mark)

Find the net force acting on 2q. a) ) 4 𝑘𝑄𝑞𝑧 (𝑧^2 +𝑑^2 ) 3 2 𝑘̂ (b) 4 𝑘𝑄𝑞𝑧 (𝑧^2 +𝑑^2 ) − 3 2 𝑘̂ (c) 4 𝑘𝑄𝑞𝑧 (𝑧^2 +𝑑^2 ) 1 2 𝑘̂ (d) 4 𝑘𝑄𝑞𝑧 (𝑧^2 +𝑑^2 ) 3 2

Two free charges 2 q and 5 q are placed apart at a distance d. to bring the system is in equilibrium, the location of the third charge must be at a distance (a) √ 2 5 d (b) √^2 𝑑 √ 5 − √ 2 (c) √^5 𝑑 √ 5 + √ 2 (d) √^2 𝑑 2 −√ 5
A charge q is placed at the centre of the cube. Then the flux of 𝐸⃗ through the shaded region is a) 𝑞 48 𝜖 0 (b) 𝑞 6 𝜖 0 (c) 𝑞 24 𝜖 0 (d) 𝑞 12 𝜖 0
The amount of workdone to assemble the whole configuration of four charges is a) 2 𝑘𝑞^2 𝑎

1 √^2 − 2 ) (b) 2 𝑘𝑞^2 𝑎

1 √^2

(c) 𝑘𝑞^2 𝑎

1 √ 2 − 2 ) (d) 𝑘𝑞^2 𝑎

1 √ 2

Which of the following potentials satisfy the Laplace’s equation?
1. V = 𝑥^2 − 𝑦^2 + 𝑧^2 2. V = r cos + z 3. V = rcos +  (a) 1&2 (b) 1&3 (c) 2&3 (d) 1,2&
  - q

q q q

(6- 10 each questions contains 3 marks)

A spherical charge distribution is given by (r) = {

𝑟^2 𝑎^2

(a) find the total charge inside the sphere (b) find the electric field intensity at point r < a

A positive charge Q is located at distances 𝑑 1 and 𝑑 2 from two grounded conducting half planes as shown in figure. (a) find the force acting on Q due to induced charge on the plane (b) find the amount of work done to place the charge Q, if 𝑑 1 = 𝑑 and 𝑑 2 = 2 𝑑
Find the capacitance of the cylindrical capacitor using Laplace equation (consider radius of the inner cylinder is ‘a’ and radius of the outer cylinder is ‘b’)
A charge - e placed in vacuum at a point (d,0,0). The region r ≤ 0 filled with metal. Find the electric field at a point ( 𝑑 2

Consider a solid sphere of radius R and charge density  spread over its volume uniformly. There is a cavity of radius a inside the sphere. Find the electric field inside the cavity.
State and explain Earnshaw’s theorem ( 5 marks) 𝑑 2 𝑑 1 Q d q V= R

Electromagnetic Theory I (PH403) Minor Examination: University of Hyderabad - Prof. Biswas, Exams of Electrodynamics

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