A thin semi–circular ring of radius r has a positive charge q distributed uniformly over it. The net field at the center O is

12.

An electric dipole has a fixed dipole moment , which makes angle θ with respect to the x-axis. When subjected to an electric field , it experiences a torque . When subjected to another electric field  it experiences torque . The angle θ is

• 60°

• 90°

• 30°

• 30°

In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be :

• 
• 

• CE

• CE

A capacitance of 2 μF is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 μF capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is :

• 24

• 32

• 2

• 2

This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement – 1: For a charged particle moving from point P to point Q, the net work done by an electrostatic field on the particle is independent of the path connecting point P to point Q.
Statement-2: The net work done by a conservative force on an object moving along a closed loop is zero.

• Statement-1 is true, Statement-2 is false

• Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.

• Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

• Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.

A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other tow corners. If the net electrical force on Q is zero, then Q/q equals

• 

• 1

• -1

• -1

A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The separation between its plates is ‘d’. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k₁ = 3 and thickness d/3 while the other one has dielectric constant k₂ = 6 and thickness 2d/3 . Capacitance of the capacitor is now 

• 1.8 pF 

• 45 pF

• 40.5 pF

• 40.5 pF

An electric charge 10^-3 µC is placed at the origin (0,0) of X - Y coordinate system. Two points A and B are situated at  and (2, 0) respectively. The potential difference between the points A and B will be

• 9 volt

• 0 volt

• 2 volt

• 2 volt

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be

• 1

• 2

• 1/4

• 1/4

A parallel plate condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charged to a potential V volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is

• ½ (K – 1) CV²

• CV² (K – 1) /K

• (K –1) CV²

• (K –1) CV²