Test Paper 2 Electrostatics

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Single Correct Choice Type(+3, Single Correct Choice Type(+3, 1.

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

distance 33 RR from its centre. Which of from its centre. Which of the following is a wrong statement?the following is a wrong statement? (A)

(A) Potential aPotential at P ist P is KQKQ 2R 2R (B)

(B) Magnitude of eleMagnitude of electric field at P may be greactric field at P may be greater thanter than 33 KQKQ₂₂ 8R 8R (C)

(C) Magnitude of electric field at P must be equal toMagnitude of electric field at P must be equal to 33 KQKQ₂₂ 8R 8R (D)

(D) Magnitude of electric field at P cannot be less thanMagnitude of electric field at P cannot be less than 33 KQKQ₂₂ 8R 8R 2.

2. The The electric electric field field in in a a region region is is given given by by the the vector vector EE ((44iiˆˆ 33 jj))ˆˆ NN .. C C



 

=

++

_

_{ }



 

G G

The maximum drop in potential The maximum drop in potential will be along

will be along (A)

(A) X-axis X-axis (B) (B) Y-axisY-axis (C)

(C) the the line line 4y 4y = = 3x 3x (D) (D) the the line line 3y 3y = = 4x4x 3.

3. The The graph graph E-r E-r corresponding corresponding to to V-r V-r graphgraph is is 22 1 1 22 33 44 55 v v r r (A) (A) 1 1 1 1 2 2 3 3 4 4 55 E E r r (B) (B) +1 +1 1 1 22 33 44 55 E E r r –2 –2 (C) (C) +1 +1 1 1 2 2 3 3 4 4 55 E E r r 1 1 (D) (D) 1 1 22 3 3 44 55 E E r r –2 –2 -1 -1 4.

4. The The charge charge per per unit unit length length of of the the four four quadrant quadrant of of the the ring ring is is 22

λλ

,,

−−

22

λλ

,,

λλ

and

λλ

respectively. The electric field at the centre is:respectively. The electric field at the centre is: (A) (A)

−−

0 0 ˆˆii 2 2 RR

λλ

πε

(B)(B) 22 ₀₀RR j jˆˆ

λλ

πε

(C) (C)

−−

0 0 2 2 _ˆˆii 4 4 RR

λλ

πε

(D) none of these(D) none of these

R R XX y y 2 2 2 2 + + 5.

5. The The diagram diagram shows shows a a small small bead bead of of mass mass m m carrying carrying charge charge q. q. TheThe bead can freely move on the smooth fixed ring

bead can freely move on the smooth fixed ring placed on a smoothplaced on a smooth horizontal plane. In the same plane a charge +Q

horizontal plane. In the same plane a charge +Q has also been fixed ashas also been fixed as shown. The potential at the point P

shown. The potential at the point P due to +Q is V. due to +Q is V. The velocity withThe velocity with which the bead should be projected from the point P

which the bead should be projected from the point P so that it canso that it can complete a circle should be greater than: (Assume gravity free space) complete a circle should be greater than: (Assume gravity free space)

a a _4a_4a +Q +Q P P (A) (A) 6qV6qV m m (B)(B) qV qV m m (C) (C) 3qV3qV m

m (D) none of these(D) none of these 1)

1)

−λ −λ

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6. Two balls, each carrying a charge q are suspended by equal insulated strings of lengthA_{m from the}

hook of a stand. This arrangement is carried in a satellite in space. The tension in each string will be (A) ₂ 2 0 4 q 4 1 A

πε

(B) 2 2 0 q 4 1 A

πε

(C) 2 2 0 2 q 4 1 A

πε

(D) zero

7. A charge q1exerts certain force on a second charge q2. If third charge q3is brought near, the force of

q1exerted on q2

(A) decreases (B) increases

(C) remain unchanged

(D) increases if q3is of same sign as q1 decreases if q2is 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 _2q _+q +2q +q O C B A

9. 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

(A) 2 2 o q _ˆ ( j) 2

π ε

R

−

(B) 2 o 2 q _ˆ (–j) R

π ε

(C) 2 2 o q _ˆ ( i ) 2

π ε

R

−

(D) 2 o 2 2 q _ˆ ( i ) R

π ε

++ ++ + O y x

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

(A) 3 0 q m L

π

πε

(B) 3 0 q 4

π

m

πε

L (C) 3 0 2q m L

π

πε

(D) 3 0 q 2

π

m

πε

L 11. Which Ex-x graph is appropriate for two

parallel long straight line charges of linear charge densities

+ λ

and –

λ

?

y O O –

λ

+λ

(–a,0) (+a,0) (A) E –a +a x (B) E +a –a x E (C) E –a +a x (D) E x D

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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

=

∫

dV; since V = C, no work is done on equipotential surface because F_el

⊥

ds.

JJG JJJG

Based on the above facts answer the following questions:

V = C E

12. The circular equipotential lines are given such that Vr

=

60. Then, the field at a distance r is

V-pattern r G (A) 60₂ ˆr r (B) r 0 (C) 60 r –1 (D) none of these 13. Since V = C on an equipotential surface, E

G

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)

+q _–2q (a, 0)

+ –

y

x

(A) circle (B) ellipse

(C) hyperbola (D) closed curves Multiple Correct Choice Type(+4,

15. In the given field pattern (A) E₁

>

E₂ (B) E₁

<

E₂ (C) V₁

>

V₂ (D) V₁

<

V₂ 1 • •2

16. 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 3 KQ₂ 8R (C) Magnitude of electric field at P must be equal to 3 KQ₂

8R (D) Magnitude of electric field at P cannot be less than 3 KQ

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Integer Type(+5,

17. A point chage q

= µ

50 Cis located in the x – y plane at the point of position vector rG₀

= +

2iˆ 3 jˆ. If the electric field at the point of position vector rG

= −

8iˆ 5 jˆ is C × 900 V

m, then find the value of C. 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

≈

1.5) a

2 1

x

19. A ring of radius R = 3m carries a charge 6

q

=

10 C− uniformly distributed over it. A long, thin wire carrying charge

λ =

10 C / m−6 per unit length of it is held along its axis with one end coinciding with the centre of the ring. If the interaction force between the ring and the thread is M × 10 –3Newton, then find the value of M.

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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