Electric Charges and Fields

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.

Two infinite identical charged sheets and a charged spherical body of charge density ' ' are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is: [figure]

1. | EA | = | EB |; EC > ED
2. EA = EB; EC = ED
3. EC ED; EA > EB
4. EA > EB; EC = ED

Two small spherical balls of mass 10 g each with charges -2 and 2 , are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite non-conducting charge sheet with uniform charge density of 100 /m2 such that length of rod makes an angle of 30 with electric field generated by charge sheet. Net torque acting on the rod is: (Take 0 = 8.85 10-12 C2/Nm2)

1. 1.12 Nm
2. 2.24 Nm
3. 11.2 Nm
4. 112 Nm

A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB at 'O' is 'E' in magnitude. What would be the magnitude of electric field at 'O' due to arc ABC ? [figure]

1. 2E
2. Zero
3. E/2
4. 2E

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density + and -2 . The force experienced by a point charge +q placed at the mid point between two plates will be: [figure]

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

A point charge +q is placed at the origin. A second point charge +9q is placed at (d, 0, 0) in Cartesian coordinate system. The point in between them where the electric field vanishes is:

1. (3d/4, 0, 0)
2. (d/4, 0, 0)
3. (4d/3, 0, 0)
4. (d/3, 0, 0)

A small bob of mass 100 mg and charge +10 is connected to an insulating string of length 1 m. It is brought near to an infinitely long non-conducting sheet of charge density ' ' as shown in figure. If string subtends an angle of 45 with the sheet at equilibrium the charge density of sheet will be: (Given, 0 = 8.85 10-12 Fm and acceleration due to gravity, g = 10 ms2) [figure]

1. 1.77 nC/m2
2. 0.885 nC/m2
3. 885 nC/m2
4. 17.7 nC/m2

Consider a circular loop that is uniformly charged and has a radius a 2. Find the position along the positive z-axis of the Cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy plane at the origin :

1. a
2. a/2
3. 0
4. a/ 2

An electric dipole of mass m, charge q, and length l is placed in a uniform electric field E = E0 i. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :

1. 12 ml2qE0
2. 2 ml2qE0
3. 2 mlqE0
4. 12 2mlqE0