Assignment#4 Applied Physics (BCS-1)

Assignment#4

Applied Physics (BCS-1)Instructor: Junaid Saif Khan

Due Date24th November 2020

Sections: CS1: A+B (Code: EE117) Fall 2020 Maximum Marks: 60

Roll No.: NAME:

Instructions:

(i) Assignment should be hand-written. Typed assignment will not be accepted.

(ii) Please attach this page with your solved assignment.

(iii) MENTION YOUR SECTION AT THE TOP of the first page of the assignment.

(iv) Solve questions on only A4 size white papers. I don’t accept any assignments otherthan this.

(v) Avoid plagiarism. Mention reference properly at the end of each question.

(vi) Make diagrams wherever possible.

1. An electroscope for the detection and measurement of electric charge consists of a fixedcork ball and a suspended cork ball (see Fig. 1). The mass of the suspended ball is1.5×10−4 kg, and the length of the suspension thread is 10 cm. The fixed ball is located10 cm directly below the point of suspension of the suspended ball. Assume that whenequal electric charges are placed on the two balls, the electric repulsive force pushes thesuspended ball up so its thread makes an angle of 45° with the vertical. What is themagnitude of the electric charge? [10]

Figure 1: A charge suspended by a thread and a fixed charge.

Due Date: 24th November 2020 Please go on to the next page. . .

Applied Physics (BCS-1: A+B) Assignment 4 Page 2 of 10

2. Four point charges of ±Q are arranged on the corners of a square of side L as illustratedin below Figure. What is the net electric force that these charges exert on a point chargeq placed at the center of the square? [10]

3. A spherical shell has net charge only on its inner and outer surfaces. The total chargeon the entire shell is Qtotal = −1.0 × 10−8 C. The charge on the inner surface of theshell is Qinner = +2.0× 10−8 C. What charge is on the outer surface of the shell? [05]

4. Find out the expression for the electric field of a quadrupole and verify that it varieswith 1/r4. [10]

5. Four closed surfaces, S1 through S4, together with the charges −2Q , Q , and −Q aresketched in following figure:

(i) Find the electric flux through each surface.

(ii) Also sketch the electric flux corresponding to each surface.

[10+5]

6. A particle with charge Q is located immediately above the center of the flat face of ahemisphere of radius R as shown in below figure. What is the electric flux through

1. the curved surface?

2. the flat face?

[5+5]





Solutions:

Question No. 1:









Question No. 2:

Due to the symmetry of the situation, the vertical componentsare equal in magnitude, but oppositely directed. Thus theycancel. The x components of each of these forces is directedparallel to the positive x axis as shown in the figure.The force on the test charge due to any one of charge is:

Fx =1

4πε0

Qq

(L√2

2)2

cos θ (1)

Whereas,

cos θ =L2

L√2

2

=

√2

2(2)

Thus Eq. 1 becomes:

Fx =1

4πε0

Qq

(L√2

2)2

√2

2(3)

By superposition principle of electric forces, the net force alongx axis on the test charge is given by:

Fx = 41

4πε0

Qq

(L√2

2)2

√2

2(4)

Fx = 4√

21

4πε0

Qq

L2(5)

Therefore, the net force on the charge +q is

~F = 4√

21

4πε0

Qq

L2~i (6)



Question No. 3:

Qouter = Qtotal −Qinner = (−1.0× 10−8C)− (+2.0× 10−8C) = −3.0× 10−8C (7)

Question No. 4:

Question No. 5:



Question No. 6:

Due Date: 24th November 2020 End of assignment

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Assignment#4 Applied Physics (BCS-1)