Electric Charge

If there are point charges , then each of them will produce the same intensity at any point which it would have produced in the absence of other point charges.
Hence, total intensity will be vector sum of produced at a point.


The given series is a geometric progression.
Hence, sum where a is first term of series and the common difference.


Total intensity

Step 1: Understanding Charge Polarity
Charges are classified into two types: positive and negative.
The property that differentiates these two types is called the polarity of charge.
Positive and negative charges attract each other, while like charges repel.
Step 2: Why Other Options are Incorrect
Option (a) refers to the amount of charge, not the type.
Option (c) is incorrect as there is no concept of "fraction of charge" in charge differentiation.

Option (d) is incorrect as polarity is the correct term.

Step 3: Conclusion
Thus, the property that differentiates two kinds of charges is their polarity.

Step 1: Understanding Dielectrics
A dielectric is a material that does not conduct electricity (i.e., it does not allow the flow of charges), but it permits electrostatic forces to act through it.
Dielectrics are insulating materials that are used in capacitors to increase their capacitance by reducing the electric field between the plates.
Step 2: Why Other Options are Incorrect
Option (a) refers to a molecule that has a permanent dipole moment, but it doesn't directly describe the behavior of charge flow.
Option (c) refers to a molecule without a permanent dipole moment, which is not relevant to the question.

Option (d) refers to a condition where the electric potential is the same everywhere, which does not describe the substance in question.

Step 3: Conclusion
Thus, the substance described in the question is a dielectric.

Step 1: Understanding the Process
When a glass rod is rubbed with silk, electrons from the glass rod are transferred to the silk.
This results in the glass rod becoming positively charged and the silk becoming negatively charged.
Step 2: Why Other Options are Incorrect
Option (a) is incorrect as protons do not transfer between objects during rubbing; only electrons are transferred.

Option (b) is incorrect because the glass rod loses electrons, not gains them.

Option (d) is incorrect because protons are not transferred in this process.

Step 3: Conclusion
Thus, when a glass rod is rubbed with silk, the glass rod gives electrons to the silk.

Step 1: Using Coulomb’s Law
The force between two point charges is given by Coulomb’s law: Where:
is the force,
is Coulomb's constant,
and are the magnitudes of the charges,
is the distance between the charges.

Step 2: Effect of Changing Distance and Charges
When the distance is cut to one-fourth, the new distance .
When the charges are doubled, the new charges are and .
The new force is:
Step 3: Conclusion
Thus, the new force between the charges is .