Test Paper 2 Electrostatics

ELECTROSTATICS-2 Single Correct Choice Type(+3, 1) 1. Charge Q is distributed non-uniformly over a ring of radius R, P is a point on the axis of ring at a distance 3 R from its centre. Which of the following is a wrong statement? (A) Potential at at P is

KQ 2R 3 KQ

(B) Magnitude of electric electric field at P may be greater greater than (C) Magnitude of electric field at P must be equal to

8R2

3 KQ 8R2 3 KQ

(D) Magnitude of electric field at P cannot be less than

8R2

G

2.

will be along (A) X-axis (C) the line 4y = 3x 3.

 N  The maximum drop in potential . C

The electric field in a region is given by the vector E = ( 4ˆi + 3ˆj ) 

(B) Y-axis (D) the line 3y = 4x

The graph E-r corresponding to V-r graph is

v 2

1

(A)

E

(B)

2

3

4

r 

5

E +1

1 1

2

3

4

1

r 

5

2

3

4

r 

5

 –2

(C)

E

(D)

E  –2

+1

3

1

2

3

4

5

1

r 

4

5

2

r 

-1

1

4.

The charge per unit length of the four quadrant of the ring is 2λ, −2λ, λ and λ respectively. The electric field at the centre is: (A) −

λ ˆ i 2πε0R

2λ ˆ i (C) − 4πε0R

(B)

y

2

2

λ ˆ  j 2πε0R X

R

(D) none of these +

5.

The diagram shows a small bead of mass m carrying charge q. The bead can freely move on the smooth fixed ring placed on a smooth horizontal plane. In the same plane a charge +Q has also been fixed as shown. The potential at the point P due to +Q is V. The velocity with which the bead should be projected from the point P so that it can complete a circle should be greater than: (Assume gravity free space) (A) (C)

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6qV m 3qV m

(B)

+Q a

4a

P

qV m

(D) none of these

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ELECTROSTATICS-2 6.

Two balls, each carrying a charge q are suspended by equal insulated strings of length A m from the hook of a stand. This arrangement is carried in a satellite in space. The tension in each string will be (A)

q2

1

(B)

4πε0 4A 2

(C)

q2

1

q2

1

4 πε0 A 2

(D) zero

4πε0 2A 2

7.

A charge q1 exerts certain force on a second charge q2. If third charge q3 is brought near, the force of  q1 exerted on q2 (A) decreases (B) increases (C) remain unchanged (D) increases if q3 is of same sign as q1 decreases if q2 is of opposite sign.

8.

Four charges are arranged at the corners of a square  ABCD as shown in the figure. The force on the charge kept at the centre O is (A) zero (B) along the diagonal AC (C) along the diagonal BD (D) perpendicular to side AB

9.

A

+q

O

D

q 2π

2

ε oR

2

( − ˆi )

(D)

2q

π ε oR 2 2

C +q

2q

Charges q and –q are uniformly distributed on the two halves of  a semicircular ring, as shown in the figure Radius of the ring is R, electric field at its centre is q q ˆj) ˆ ( − (A) (B) (–j) 2 π ε oR 2 2π2εoR2 (C)

+2q B

y

+ +

+

++

O

x

( ˆi )

10.

A particle of mass m and charge q is located midway between two fixed charged particles each having a charge q and at a distance 2L apart so that distance of this charge from each charge located at end is L. Assuming that the middle charge moves along the line joining the fixed charges. The frequency of oscillation when it is displaced slightly is q q 2q q (A) (B) (C) (D) π mπε0L3 4π mπε0 L3 2π mπε0 L3 π mπε0 L3

11.

Which Ex -x graph is appropriate for two parallel long straight line charges of  linear charge densities + λ and  –λ ?

y  – λ

+λ O (–a,0)

(A)

(C)

+a

+a

(D)

+a

x

E  –a

x

E

 –a

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(B)

E

 –a

O (+a,0)

x

E E x

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ELECTROSTATICS-2 Paragraph for Questions 12 to 14 Equipotential surfaces are the planes where potential is constant for any point in the plane. The potential at any point on the equipotential surface is the net potential of all charges of the system given as V JJG

since V = C, no work is done on equipotential surface because Fel following questions:

JJJG

= ∫ dV;

⊥ ds. Based on the above facts answer the

E

V=C

12.

The circular equipotential lines are given such that Vr = 60. Then, the field at a distance r is V-pattern G

r 

60 rˆ  r 2  –1 (C) 60 r 

0

(A)

(B) r 

(D) none of these G

13.

Since V = C on an equipotential surface, E at any point of the equipotential surface is (A) zero (B) perpendicular to the equipotential surface (C) non-zero along equipotential surface (D) > 0

14.

The shape of equipotential lines for V = 0 of the given charge configuration is (in the x-y plane) y + +q

(A) circle (C) hyperbola

(a, 0)  –  –2q

x

(B) ellipse (D) closed curves

Multiple Correct Choice Type(+4, 1) 15. In the given field pattern (A) E1 > E2

< E2 (C) V1 > V2 (D) V1 < V2 (B) E1

16.

•1

•2

Charge Q is distributed non-uniformly over a ring of radius R, P is a point on the axis of ring at a distance

3 R from its centre. Which of t he following are correct statement(s)?

(A) Potential at P is

KQ 2R

(B) Magnitude of electric field at P may be greater than (C) Magnitude of electric field at P must be equal to

8R2

3 KQ 8R2

(D) Magnitude of electric field at P cannot be less than FIITJEE

3 KQ

3 KQ 8R2

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ELECTROSTATICS-2 Integer Type(+5, 1) G 17. A point chage q = 50µC is located in the x – y plane at the point of position vector r0 G

electric field at the point of position vector  r 18.

In the given electric field lines, the point where field is zero ( null-point) is at a distance x (in cm), say. Then find x. (a = 2cm and take 2

19.

≈ 1.5 )

= 8iˆ − 5ˆj is C × 900

x

1

= 2iˆ + 3ˆj . If the

V , then find the value of C. m

a

2

A ring of radius R = 3m carries a charge q = 10 −6 C uniformly distributed over it. A long, thin wire carrying charge λ = 10−6 C / m per unit length of it is held along its axis with one end coinciding with  –3 the centre of the ring. If the interaction force between the ring and the thread is M × 10 Newton, then find the value of M.

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ELECTROSTATICS-2  Answers 1. C 2. C 3. B 4. A 5. A 6. A 7. C 8. C 9. B 10. D 11. C 12. A 13. B 14. A 15. A, C 16. A, B, D 17. 5 18. 4 or 5 19. 3

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