Electrostatic Potential And Capacitance

Step 1: Understanding the Effect of Dielectric on a Disconnected Capacitor Since the capacitor is disconnected from the battery, its charge remains constant. The charge on the capacitor is given by: Step 2: Effect of Introducing the Dielectric When a dielectric material with dielectric constant is introduced, the capacitance of the capacitor increases as: However, since the charge remains constant, the new potential across the capacitor is given by: Thus, the final charge remains , and the new potential is .

Step 1: Understanding the Principle of a Meter Bridge A meter bridge works on the principle of the Wheatstone bridge: where:
- is the unknown resistance in the left gap.
- is the resistance in the right gap.
- is the initial balance length (null point), given as cm.

Step 2: Applying the Given Condition If the resistance in the left gap is increased by 100%, the new resistance becomes . The new balance length is found using: Dividing both equations: Substituting : Solving for :

Step 3: Calculating Percentage Increase Thus, the correct answer is .

Step 1: Understanding Electric Flux The electric flux ( ) is given by the dot product of the electric field vector ( ) and the area vector ( ):

Step 2: Identifying the Perpendicular Component of Since the area lies in the XZ plane, its normal vector is along the direction (Y-axis). The electric field component along is 13 NC , which is the -component of .

Step 3: Calculating Electric Flux The electric flux is: Thus, the correct answer is:

Step 1: The capacitance of a parallel plate capacitor is given by the formula: where is the permittivity of free space, is the area of the plates, and is the separation between the plates.

Step 2: When the distance between the plates is halved, the capacitance doubles. Moreover, when a dielectric material is inserted, the capacitance increases by the factor of the dielectric constant .

Step 3: The new capacitance is: where and .

Step 1: The electrostatic force between two charges is given by Coulomb's law: where and are the charges, is the distance between them, and is Coulomb's constant.

Step 2: Initially, the force between the two charges is .

Step 3: After the balls are brought into contact, the charges redistribute equally, so:

Step 4: From the equation, we find that:

Step 5: The ratio of charges is .