ELECTROSTATICS This section contains multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
1.
A capacitor is made of two concentric spherical shells A and B of radii a and b respectively, where a < b. The external shell B is grounded. Inner shell i.e., (r a) is filled with a uniform positive charge of density . Variation of electric field versus distance from the centre. E
E
(A)
(B) a
b
r
a
E
b
r
E
(C)
(D) a
b
r
a
r A
2.
3.
4.
In circuit diagram capacitance of capacitor C2 C1 C1 3F and C 2 1F . It is given that time C2 C1 constant of circuit between A and B is 3 C1 millisecond. Value of R will be (A) 1 C2 (B) 10 (C) 100 (D) 1000 As shown in circuit diagram an ideal voltmeter Box and an ideal ammeter reading are zero. Sum of 12Volt potential drop across box and 5 resistances will be (given that there are no fault in voltmeter A and ammeter) (A) 7 volt (B) 5 volt (C) 12 volt (D) Data insufficient For maximum power from battery the internal resistance of battery r is R R
R
R
R R R
R R
r
(A) 10 R (C) R/8
4R 9 (D) 10R/9 (B)
R
B
R
V
5.
6.
Two concentric spherical shells A and B are kept as shown with the switch open. The potentials at A and B are 5 V and 3 V respectively. If the switch is closed, then potential of sphere A will become (A) 5 V (B) 3 V (C) 2 V (D) 7 V In the circuit shown, the readings of the ammeter and voltmeter are (A) 6 A, 60 V (B) 0.6 A, 6V 6 60 (C) 6 A, 6 V (D) A, V 11 11
B A S
6V, 1
A
V
7.
8.
9.
10.
11.
12.
In the given circuit, when key K is open, reading of ammeter is I. Now key K is closed then the correct statement is : (A) If 1 < IR, reading of the ammeter is less than I (B) If IR < 1 < 2IR, reading of the ammeter is greater than I (C) If 1 = 2IR, reading of the ammeter will be zero (D) Reading of ammeter will not change Time constant of charging of the capacitor shown in the adjoining figure is (A) 2 RC (B) CR/2 (C) zero (D) infinite
R
R
A K
R
R
In meter bridge or wheat stone bridge for measurement of C resistance, the unknown and the known resistance are E S interchanged. The error so removed is (A) End Correction (B) Index error (C) Out to temperature effect (D) Random error A parallel-plate capacitor, filled with a dielectric of dielectric constant k, is charged to a potential V0. It is now disconnected from the cell and the slab is removed. If it now discharges, with time constant , through a resistance, the potential difference across it will be V0 after time (A) k (B) ln k 1 (C) ln 1 (D) ln (k 1) k A uniform electric field of 4 V/m is directed at 450 to the x-axis along the vector 1i 1j . Considered the points A(0, 2) and B (3, 0). The potential difference VA – VB is given by (a) 0 (b) 4 V (c) 6.4 V (d) 2.8 V An ellipsoidal cavity is present inside a solid conducting sphere centered at the origin. The radius of the sphere is R and it is electrically neutral. On the XY plane, the equation of the cavity can be given by the equation X2/a2 + Y2/b2 = 1. If a point charge +Q is placed at the centre of the cavity then what is the potential of the point A{having coordinates (0, b)} due to induced charges on ellipsoidal surface? Y
+Q
(a) (Q/4π0)(1/b – 1/R)
X
(b) (Q/4π0)(1/b + 1/R)
13.
(c) (Q/4π0)(– 1/b) (d) Q/4π0R The diagram shows V versus X graph. Which of the following graphs most appropriately represent the E versus X graph? V X
Parabolic E
E
(a)
(b) X
X
E
E
(c)
(d) X X
14.
Three infinitely long charge sheets are placed as shown in figure. The electric field at point P is:
(a) 15.
2 k 0
(b)
2 k 0
(c)
4 k 0
(d)
4 k 0
A non-conducting ring of radius 0.5 m carries a total charge of 1.11 10 10 C distributed non-uniformly on its circumference producing an electric field E everywhere is space. The value of the l 0 integral E.dl (l = 0 being centre of the ring) in volt is: l=
(a) +2
(b) –2
(c)
1 2
(d) zero
16.
Charge Q is divided into two parts which are then kept some distance apart. The force between them will be maximum if eth two parts are (A) Q/2 each (B) Q/4 and 3Q/4 (C) Q/3 and 2Q/3 (D) e and (Q – e), where e = electronic charge
17.
For the circuit shown, find the potential difference between A and B 2E (A) E (B) 3 2E (C) (D) zero 5
18.
A
C E C B C
C
For a uniformly charged conducting solid cylinder of infinite length, which of the following graph shows the variation of E with r ? (distance from axis)
E
E E
(A) E
E
1 r2 r
(D)
E
E r
1 r r
R
E
R
19.
E r
(B)
r
R
(C)
1 r
E R
1 r2 r 1cm
In the arrangement of a pair of parallel plates having separation 1 cm as shown. What is electric field in the region between the plates ? (A) 15 kN/C towards right (B) 15 kN/C towards left (C) 25 kN/C towards right (D) 25 kN/C towards left
-50V
20.
21.
22.
A charge Q is placed at P (0, 0, a). The coordinates of A and C a of a square are 0, , 0 and (a, a, 0) respectively. The flux 2 through ABCD is Q Q (A) (B) 16 o 24 o Q (C) (D) none of these 48o
z
Q
Pz(0, 0, a)
a
A(0, 2 , 0) B
O
x E
D
p Q
(D)
1 CV2 (1 – k) 4
A spherically symmetric charge distribution is given by. r 0 1 when r a a 0 when r a For what value of r is the field will be maximum
r
l
A capacitor of capacitance C is charged by a battery of emf V and then disconnected. The work done by an external agent to insert a dielectric of dielectric strength k of half the length of the capacitor is k – 1 1 – k 1 1 (A) CV2 (B) CV2 2 2 k 1 k 1
1 CV2 (k – 1) 4
y
C(a, a, 0)
A dipole of dipole moment p is placed at a distance r from a point charge Q (as shown in figure). Choose the incorrect statement. (A) Torque acting on the dipole is zero (B) Force acting on the dipole due to the electric field produced by Q is zero. Qp (C) Potential energy of the dipole due to the point charge Q is 4o r 2 Qp (D) Force acting on the dipole due to the point charge Q is 2o r 3
(C)
23.
+200V
l 2
l 2
(a) r
a 2
(b) r
a 3
(c) r
2a
(d) r
3
2a 3
This section contains multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which MORE THAN ONE IS/ARE CORRECT.
24.
A parallel plate capacitor with plate area A and separation d has charge Q. A slab of dielectric constant k is inserted in space between the plates almost completely fills the space. If E0 and C0 be the electric field and capacitance before inserting the slab, then E (A) the electric field after inserting the slab is 0 k (B) the capacitance after inserting the slab is k C0 1 (C) the induced charge on the slab is Q 1 k U (D) the energy stored in the capacitor becomes 0 , U0 being the energy of the capacitor k before inserting the slab
25.
In the circuit shown, a potential difference of 100 V is applied across AB. Then (A) the potential difference between points C and D is 50 V 100V (B) the potential difference between A and C is 25 V (C) the potential difference between B and D is 25 V (D) all the capacitors have equal charge
26.
27.
28.
Three very large plates are given charges as shown in the figure. If the cross-sectional area of each plate is the same, then the final charge distribution on the surface of the plates a, b, c, d, e, f is (A) 7Q on surface e and 3Q on surface f (B) -2Q on surface b and 3Q on surface a (C) -7Q on surface d and 2Q on surface c (D) the magnitude of charges at all surfaces b, c, d, e is equal
(c) The force Q2 is k
30.
C C
C 2C D
B
Q
a
b
–5Q
10Q
c
e
A
d
B
f
C
A particle of mass m and charge –q is projected from the origin with a horizontal speed v into an electric field of intensity E directed downward. Choose the correct statements. (a) The kinetic energy after a displacement y along y-axis is qEy (b) The horizontal and vertical components of acceleration are ax = 0, ay = qE/m (c) The equation of trajectory is y = 0.5 (qEx2/mv2) (d) All the above are correct Charges Q1 and Q2 are placed inside and out side respectively of an uncharged conducting shell. Their separation is r. (a) The force on Q1 is zero
29.
2C
A
Q1Q2 r2
(b) The force on Q1 is k
Q1Q2 r2
(d) The force on Q2 is zero
A conductor with a cavity is placed inside a non-uniform electric field (a) the electric field inside the conductor is zero, but non zero in the cavity (b) the total charge on the conductor is zero (c) the total charge on the conductors is non zero (d) the electric field inside the conductor as well as cavity is zero A conducting disc is rotated with angular velocity about vertical axis. (a) the center is at higher potential than periphery
31.
(b) the electric field inside the disc is zero (c) the electric field inside the disc is non zero (d) the center is at lower potential than periphery In the circuit shown in figure, R1 = R2 = R3 = R. Switch is closed at time t = 0. Then (A) Potential difference across R2 is equal to potential CR difference across R3 at t ln(2) 2 (B) Maximum current through R3 is V/2R (C) Minimum current through R3 is V/2R V (D) Maximum charge stored in the capacitor is C 2
R1 C
V
R3 S
R2
32.
In a potentiometer arrangement E 1 is the cell establishing current in primary circuit. E2 is the cell to be measured. AB is the potentiometer wire and G is a galvanometer. Which of the following are the essential conditions for balance to be obtained (A) The e.m.f. of E1 must be greater than the e.m.f. of E2 (B) Either the positive terminals of both E1 and E2 or the negative terminals of both E1 and E2 must be joined to one end of potentiometer wire (C) The e.m.f. E2 must be greater then E1 (D) Terminals can be joined in any manner
33.
Three ammeters A, B and C of resistances RA, RB and RC T respectively are joined as shown in the figure. When some potential 1 difference is applied across the terminals T1 and T2, their readings are IA, IB and IC respectively (A) IA = IB (B) I A R A I BR B I C R C I R I RC (C) A C (D) B IC R A IC R A R B
A
34.
B T2 C
A voltmeter and an ammeter are joined in series to an ideal cell, giving readings V and A respectively. If a resistance equal to the resistance of the ammeter is now joined in parallel to the ammeter (A) V will not change (B) V will increase slightly (C) A will become exactly half of its initial value (D) A will become slightly more than half of its initial value
