Electric Charges and Fields

Two point charges q1=3 μC and q2=-4 μC are placed at points (2 i+3 j+3 k ) and ( i+ j+ k ) respectively. Force on charge q2 is N. (Take 14 0=9 109 SI Units)

1. (12 i+24 j+24 k ) 10-3
2. (4 i+8 j+8 k ) 10-3
3. (3 i+6 j+6 k ) 10-3
4. (-4 i-8 j-8 k ) 10-3

A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value of Q is nC. ( 0=8.85 10-12 C2/Nm2 and =3.14)

1. 2.14
2. 2.44
3. 3.25
4. 0.7

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field E1=E0 x. If another electric field E2=2E0 ( y+ z ) is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

1. 73%
2. 63%
3. 83%
4. 53%

Two short electric dipoles A and B having dipole moment p1 and p2 respectively are placed with their axes mutually perpendicular as shown in the figure. The resultant electric field at a point x is making an angle of 60 with the line joining points O and x. The ratio of the dipole moments p2/p1 is . [figure]

1. 32
2. 2 3
3. 1 3
4. 3

Two point charges 8 μC and -2 μC are located at x=2 cm and x=4 cm, respectively on the x-axis. The ratio of electric flux due to these charges through two spheres of radii 3 cm and 5 cm with their centers at the origin is .

1. 4 : 1
2. 3 : 4
3. 4 : 3
4. 4 : 5

Identify the correct statements : Choose the correct answer from the options given below :

1. A, C, E Only
2. A, B, D, E Only
3. B, C, D, E Only
4. A, B, C, D Only

The electrostatic potential in a charged spherical region of radius r varies as V = ar3 + b, where a and b are constants. The total charge in the sphere of unit radius is a 0. The value of is . (permittivity of vacuum is 0)

1. -12
2. -8
3. -9
4. -6

Three charges +2q, +3q and -4q are situated at (0, -3a), (2a, 0) and (-2a, 0) respectively in the xy plane. The resultant dipole moment about origin is .

1. 2qa(7 i - 3 j)
2. 2qa(3 j - 7 i)
3. 2qa(3 i - 7 j)
4. 2qa(3 j - i)

A point charge q = 1 is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q = 24 , distributed uniformly along its length, as shown in figure. Force between q and wire is N. (Use : 14 0 = 9 109 N m2/C2) [figure]

Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is: [figure]

1. 3q2 0
2. 3q4 0
3. q 0
4. 3q 0