Electric Fields, Capacitors, and Related Concepts – Step-by-Step Physics Guidance

Q4. The figure shows electric field lines arising from two small charged particles P and Q. Consider the following two statements:

• (i) The charge on P is smaller than the charge on Q.

• (ii) The electrostatic force on P is smaller than the force on Q.

Which is true?

Background

Topic: Electric Field Lines and Electrostatic Forces

This question tests your understanding of how electric field lines represent charge magnitude and how the force on a charge relates to the electric field.

Key Terms and Formulas

• Electric field lines: The number of lines emerging from a charge is proportional to the magnitude of the charge.

• Electrostatic force: $F = qE$ where $q$ is the charge and $E$ is the electric field strength.

Step-by-Step Guidance

1. Observe the number of field lines emerging from P and Q. More lines indicate a larger charge magnitude.

2. Recall that the force experienced by a charge in an electric field depends on both the charge and the field strength at its location.

3. Compare the statements: (i) relates to charge magnitude, (ii) relates to the force experienced by each charge.

4. Think about whether the field lines and their density support either statement, and whether the force on each charge can be inferred from the diagram.

Try solving on your own before revealing the answer!

Final Answer: (a) Only (i) is true.

The number of field lines indicates that Q has a larger charge than P, so statement (i) is true. The force on each charge depends on the field created by the other, not the field lines shown, so statement (ii) is not necessarily true.

Q8. The figure shows two parallel-plate capacitors storing the same amount of charge Q. The plates of each capacitor are separated by the same distance, and their areas are identical. Capacitor 2 is filled with a dielectric material with dielectric constant κ (> 1). Consider the following statements:

• (i) The capacitance of Capacitor 1 is larger than that of Capacitor 2.

• (ii) The potential energy stored in Capacitor 1 is larger than that in Capacitor 2.

Which is true?

Background

Topic: Capacitance and Dielectrics

This question tests your understanding of how a dielectric affects capacitance and stored energy in a capacitor.

Key Terms and Formulas

• Capacitance without dielectric: $C_1 = \varepsilon_0 \frac{A}{d}$

• Capacitance with dielectric: $C_2 = \kappa \varepsilon_0 \frac{A}{d}$, where $\kappa > 1$

• Potential energy stored: $U = \frac{Q^2}{2C}$

Step-by-Step Guidance

1. Recall the formula for capacitance with and without a dielectric. Compare $C_1$ and $C_2$.

2. Since both capacitors store the same charge $Q$, use the formula for potential energy to compare $U_1$ and $U_2$.

3. Analyze how the dielectric constant $\kappa$ affects the capacitance and, consequently, the stored energy.

4. Consider which statements (i) or (ii) are supported by the formulas and the physical setup.

Try solving on your own before revealing the answer!

Final Answer: (b) Only (ii) is true.

Capacitor 2, with the dielectric, has a larger capacitance ($\kappa > 1$), so statement (i) is false. For the same charge, the potential energy is lower in the capacitor with higher capacitance, so statement (ii) is true.