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 coming from each charge. 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 field lines around P and Q to determine which charge is larger.

4. Think about whether the force on P is necessarily smaller than the force on Q, based on the field and charge values.

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. However, the force on a charge depends on the field at its location, not just the charge magnitude, 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: $C_2 = \kappa \varepsilon_0 \frac{A}{d}$

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

• $\kappa$ is the dielectric constant ($\kappa > 1$)

Step-by-Step Guidance

1. Compare the capacitance formulas for both capacitors. Note how the dielectric constant affects $C_2$.

2. Since both capacitors store the same charge $Q$, use the energy formula to compare the stored energy.

3. Analyze whether $C_1$ or $C_2$ is larger, given $\kappa > 1$.

4. Determine which capacitor stores more energy, based on the relationship between capacitance and energy.

Try solving on your own before revealing the answer!

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

Capacitor 2 has a larger capacitance due to the dielectric ($\kappa > 1$), so statement (i) is false. Since $U = \frac{Q^2}{2C}$, a larger capacitance means less stored energy for the same charge, so statement (ii) is true.