Electric Charges and Fields · Question 20

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)