Electric Charges and Fields

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

Match List - I with List - II. Choose the correct answer from the options given below :

1. (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
2. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
3. (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
4. (A)-(IV), (B)-(II), (C)-(III), (D)-(I)

A point charge causes an electric flux of -2 104 N m2 C-1 to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given 0=8.85 10-12 C2 N-1 m-2)

1. 17.7 10-8 C
2. -17.7 10-8 C
3. 15.7 10-8 C
4. -15.7 10-8 C

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density 0. Choose the correct option from the following. [figure]

1. Torque on dipole is zero and net force is directed away from the sheet.
2. Potential energy of dipole is minimum and torque is zero.
3. Potential energy and torque both are maximum.
4. Torque on dipole is zero and net force acts towards the sheet.

A square loop of sides a=1 m is held normally in front of a point charge q=1 C at a distance a2. The flux of the electric field through the shaded region is 5p 1 0 N m2C, where the value of p is . [figure]

A small uncharged conducting sphere is placed in contact with an identical sphere but having 4 10-8 C charge and then removed to a distance such that the force of repulsion between them is 9 10-3 N. The distance between them is (Take 14 0 as 9 109 in SI units)

1. 1 cm
2. 2 cm
3. 4 cm
4. 3 cm

A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charge q separated by a distance 2a. For the charge particle at P not to experience any net force, which of the following correctly describes the situation? [figure]

1. ar 0.5
2. ar 3
3. ar 10
4. ar 20