Electric Charges and Fields

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

Two short dipoles (A, B), A having charges 2 and length 1 cm and B having charges 4 and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point P, equi-distant from the centres of both dipoles is N/C. [figure]

1. 916 2 105
2. 916 2 104
3. 9 2 104
4. 4.5 2 104

A simple pendulum has a bob with mass m and charge q. The pendulum string has negligible mass. When a uniform and horizontal electric field E is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is .

1. mg - qE
2. m2g2 + q2E2
3. mg + qE
4. m2g2 - q2E2

Six point charges are kept 60 apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is . ( 0 is permittivity of free space) [figure]

1. - ( 5Q8 0 R2 )( i - 3 j)
2. Q4 0 R2( 3 i - j)
3. - Q4 0 R2( 3 i - j)
4. - 5Q8 0 R2( i + 3 j)

An infinitely long wire has uniform linear charge density = 2 nC/m. The net flux through a Gaussian cube of side length 3 cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be x N m2 C-1, where x is: [Neglect any edge effects and use 14 0 = 9 109 SI units]

1. 6.48
2. 0.72
3. 1.44
4. 2.16

A dipole with two electric charges of 2 magnitude each, with separation distance 0.5 , is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30 from the axis, it tends to realign in the direction due to a torque. The value of torque is:

1. 2.5 10-9 Nm
2. 2.5 10-12 Nm
3. 5 10-3 Nm
4. 5 10-9 Nm

The electric field in a region is given by E = (2 i + 4 j + 6 k) 103 N/C. The flux of the field through a rectangular surface parallel to x–z plane is 6.0 Nm2C-1. The area of the surface is cm2.