Single Correct Choice Type(+3, Single Correct Choice Type(+3, 1
1.. A A uunniiffoorrm em elleeccttrriic c ffiieelldd EE
aaiiˆˆ bb jjˆˆ
, intersects a surface of area A. What is the flux through this area if , intersects a surface of area A. What is the flux through this area if the surface lies in the
the surface lies in the yzyz plane?plane?
((AA)) aaAA ((BB)) 00 ((CC)) bbAA ((DD)) A A aa22
bb222.
2. ThThe fe fieield ld liline ne to to ththe re rigight ht is is a fa fieield ld liline one of tf the ehe elelectctriric fc fieieldld, t, thehenn its representation can be:
its representation can be: (A
(A)) EE((xx,,yy))
ˆˆii ssiinn((xx))jjˆˆ
(B
(B)) EE((xx,,yy))
ˆˆii ccooss((xx))jjˆˆ
(C)
(C) EE((xx,,yy))
ˆˆii ssiinn((xx))jjˆˆ
(D)
(D) EE((xx,,yy))
ˆˆii ccooss((xx))jjˆˆ y y x x 0,0 0,0 33.. TThhe e nneet t eelleeccttrriic c ffiieelldd EE
due to the uniformly charged rod at P makes angles
due to the uniformly charged rod at P makes angles
11andand
22with AP and BPwith AP and BP respectively. Then respectively. Then
11// 22:: E E P P A A BB 2 2 1 1 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +((AA)) ==11 ((BB)) >>11 ((CC)) <<11 ((DD)) AP AP PB PB 4
4.. A A ppaarrttiicclle e oof f cchhaarrggee
q and mass m moves q and mass m moves in a circle around a long straight wire of in a circle around a long straight wire of linear chargelinear charge density +density +
. If r = radius of the circular path and T = time period of the motion in circular path. Then. If r = radius of the circular path and T = time period of the motion in circular path. Then ((AA)) T T = = 22
r(m/2Kr(m/2K
q)q)1/21/2 ((BB)) TT22= 4= 4
22mr mr 33/2qK/2qK
(C
(C)) T = T = 1/1/22
r(2Kr(2K
q/m)q/m)1/21/2 (D(D)) T = T = 1/1/22
r(m/Kqr(m/Kq
))1/21/2, where K = 1/4, where K = 1/4
005.
5. A riA ring ng chchaargrge Q e Q didiststriribbututed ed ununififorormlmly ay alolong ng itits ls lenengtgth. h. A sA smamallll portion of the ring is cut so that a little charge
portion of the ring is cut so that a little charge QQ is removed. Theis removed. The electric field at the centre is:
electric field at the centre is: (A (A)) KK Q22Q ˆˆii R R
(B) (B) KK ((Q Q 22 QQ)) ˆˆii R R
(C) (C) KK Q22Q ˆˆii R R
(D)(D) none none of of thestheseex x y y QQ R R O O 6.
6. ElElecectritric chc charargeges +qs +q, +q , +q anandd –2–2q aq are hre heleld fid fixexed ad at (0t (0, 0, 0), (), (d, d, 0) a0) and (nd (0, d0, d) re) respespectictivevely ly of a of a (x, (x, y)y) coordinate system. The electric dipole moment of the system is
coordinate system. The electric dipole moment of the system is (A)
(A) qqdd((iiˆˆ
22jj))ˆˆ (B)(B)
qqdd((iiˆˆ
22jj))ˆˆ (C)(C) qqdd((iiˆˆ
22jj))ˆˆ (D)(D) qqdd(( ii
ˆˆ 22jj))ˆˆ7
7.. ThThe e ppootteennttiiaal l V V iis vs vaaryryiinng wg wiitth h x x aannd y d y aass V V 11((y y 422 4xx)) 2
2
volt. The field at x = 1m, y = 1m, is:volt. The field at x = 1m, y = 1m, is: (A)(A) 22iiˆˆ ˆˆ
jj VV // mm (B)(B)
22iiˆˆ ˆˆjjVV // mm (C)(C) 22iiˆˆ ˆˆ
jj VV // mm (D)(D)
22iiˆˆ 22jj VˆˆV // mm8.
8. A nA negegatativive ce chahargrgee – q – q momoveves ss slolowwly ly in in a ca ciircrcululaar pr paath th frfromom position 1 to position 2. The work done by the external agent position 1 to position 2. The work done by the external agent in the electric field of + Q fixed at the origin is (take
in the electric field of + Q fixed at the origin is (take
0 0 1 1 K K 4 4
Q Q 2 2 –a –a –q –q a a 22aa 33aa + + 11((AA)) zzeerroo ((BB)) 4KQq4KQq 3a 3a (C)(C) 2KQq 2KQq 3a 3a (D)(D) 2KQq 2KQq 3a 3a
1) 1)9. T he E-x patt er n for th e give n V -x patt er n is v 0 V 10 V 20 V O 30 V 60° x (A) E x 60° (B) E x 30° (C) E x (D) E x 150°
10. Between two infinitely long wires having linear charge densities
and –
there are two points A and B as shown in the figure. The amount of work done by the electric field in moving a point charge q from A to B is equal to0(A) 0 0 q In 2 2
(B) 0 0 2 q In 2
(C) 0 0 2 q In 2
(D) 0 0 q In 2
– A B a a aParagraph for Questions 11 to 13 The potential at any point can be given as V r E dr.
This helps us to find V if E is given. If V is given at any point, E in any direction can be found by taking the derivative of V in that direction which is given as
x V E . x
Using the above formulae, answer the following questi ons.11. E varies along x as E = 3x2. If the potential at x = –1 is +3 volt, the potential at x = + 2 is
(A) –10volt (B) + 4volt
(C) –6 volt (D) – 12volt
12. In the previous question, the volume charge density at x = 1 is
(A) 6
0(B) 4
0(C) 3
0 (D) noneofthese13. If the potential at any region varies in x-y plane as 2 2
V a (x y ), which of the following field patterns is correct? (A) y x (B) y x (C) y x (D) y x
Multiple Correct Choice Type(+4,
14. A point charge q is placed at origin. Let E .E A B
and EC
be the electric field at three points A(1, 2, 3), B(1, 1, –1) and C (2, 2, 2) due to charge q. Then
(A) E A
EB (B) E || E A B (C) | E | 4 | E |B
C (D) | E | 8 | E |B
C 15. A particle of mass m and charge + q has been projected from ground as shown in the figure, such that tan mg
qE
. Mark out the correct statement (s).E
(A uniform electric field) u
y
x
(A) The path of motion of the particle is parabolic(B) The path of motion of the particle is a straight line. (C) Time of flight of the particle is 2u sin
g
(D) Range of motion of the particle is equal to
2
u sin2 . g
16. Electrostatic lines of forces:(A) cannot be closed (B) can be circular (C) never intersect
(D) terminate on –ve charges and originate from +ve charges Integer Type(+5,
17. Two identical helium filled balloons A and B fastened to a weight of 15 gram by threads float in equilibrium as shown in the figure. If the charge on each balloon is Q×10 –6 Coulomb, then find the value of Q. Assuming that they carry equal charges (take g = 10 m/s2). + + A B 1m 1m 1.2m
18. A ring of radius R = 3m carries a charge 6
q 10 C uniformly distributed over it. A long, thin wire carrying charge
10 C / m6 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.19. The bob of a pendulum has mass m = 1 kg and charge q = 40
C. Length of pendulum is = 0.9 m. The point of suspension also hasthe same charge 40
C. What the minimum speed u(in m/s) should be imparted to the bob so that it can complete vertical circle?m q u q 1) 1)
Answers 1. A ˆ S
Ai S
= E S
Aa 2. AGraph of field line represents the graph of (
cos x), so y =
cos x
dy sinx coefficient of E along y axisdx coefficient of E along x axis
E
ˆi sin xjˆ 3. AAs we know that direction of field at any point due to uniformly charged rod is along the angle bisector of the angle formed by the ends of rod at the point, So
1=
24. A FC= 2 mv r
2 0 2k q mv r r
0 1 m v
2k q
T = 0 2 r m 2 r v 2k q
r
q0 + + + + + + + + + 5. CNet electrostatic field at the centre of uniformly charged ring is zero so,
C C( Q) C(Q) E
E
E
0
C(Q) c( Q) 2 k Q ˆ E E (i ) R
x y Q R O
Q 6. C ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆP
(q)(0i
0 j) (q)(di
0 j) ( 2q)(0i
dj) qd(i 2j) 7. C V ˆ V ˆ E i j x y
= 1( 4)iˆ 1(2y)jˆ 2iˆ yjˆ 2 2
Ey 2mx 1m
2iˆ ˆj 8. D 8. U i UB KQq 3a
, U f UA KQq a
Work done by external filed U U f Ui KQq KQ q
a 3a
= 2KQq 3a A –a B +3a 9. DAs we know that field lines are perpendicular to the equi-potential line or surface, and its direction is in the direction of decreasing potential.
10. D 10. E 2K ˆi 2K ˆi 2K 1 1 (i)ˆ x 3a x x 3a x
ˆ dU
qE dxi U 2K q 2a a 1 1 dx x 3a x
2a B A a 0 0 q q U U U ln | x | ln | 3a x | ln(2) 2
Work done by electrostatic force
0 q U
ln(2)
+
– – – – – – – 3a – x + + + + + + +–
x P11. C 11. dV
Edx
3x dx2 2 2 1 dV 3x dx
V(2) – V(–1) = – 3 2 1 x
V(2) – 3 = – [8 – (–1)] = –9
V(2) = –9 + 3 = –6 Volt 12. A 2 1 3 bx
2 2 3 b(x dx)
d =
1 2 3 b[(dx) 2
2xdx] 0 bdx 6 bxdx
= 6 Second Method 0 dE dx
6x 0
= 6
x 1
6 0 x x+dx O
b E E dE 13. E
2a[xiˆ
yj]ˆ
dy y dx x
dy dx y
x
lny = – lnx + lnc
c y x
xy = C 13. B 14. A, C AO E A 3/ 2 Kq ˆ ˆ ˆ (i 2j 3k) E (14)
, BO B 3/ 2 Kq ˆ ˆ ˆ E (i j k) E (3)
, and CO 3/ 2 Kq ˆ ˆ ˆ E (2i 2 j 2k) E 8(3)
15. B, C ˆ ˆ F
mgj
qEi
a qE ˆi gjˆ m
Hence direction of velocity and acceleration will be along sam e line but opposite, so particle will m ove along straight line.
16. A, C, D
Basic definition of field lines
17. 3 2T cos
=mg ...(i) T sin
= 2 2 Kq r ...(ii) tan
= 2 2 2kq r mg 9 2 12 3 0.6 2 9 10 Q 10 0.8 1.2 1.2 15 10 10
Q = 3 18. 3 k Q F 3 R
19. 6 2 9 12 2 kq 9 10 1600 10 160 N 0.9 0.9 9
mg = 1
10 = 10 N
2 2 kQ mg
, so string behave as a rod
u
4g
4 10 0.9 6m/s0x
