Electric Field Lines, Capacitance, and Physics II Concepts Review

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 option is correct?

Background

Topic: Electric Field Lines and Electrostatic Forces

This question tests your understanding of how electric field lines relate to the magnitude of charge and the forces experienced by charged particles.

Key Terms and Formulas

• Electric Field Lines: The number of lines emerging from or converging to a charge is proportional to the magnitude of the charge.

• Electrostatic Force: The force between two charges is given by Coulomb's Law:

$F = \frac{k |q_1 q_2|}{r^2}$

• $F$ = force between charges

• $k$ = Coulomb's constant

• $q_1, q_2$ = magnitudes of the charges

• $r$ = distance between charges

Step-by-Step Guidance

1. Observe the number of electric field lines associated with 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.

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

4. Think about whether the number of field lines and the force on each charge support the truth of statements (i) and (ii).

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 experienced by each charge is equal in magnitude (Newton's third law), so statement (ii) is not 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 $\kappa (> 1)$. 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 option is correct?

Background

Topic: Capacitance and Dielectrics

This question tests your understanding of how a dielectric affects the capacitance and energy storage of a parallel-plate capacitor.

Key Terms and Formulas

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

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

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

• $\varepsilon_0$ = permittivity of free space

• $A$ = plate area

• $d$ = plate separation

• $\kappa$ = dielectric constant ($>1$)

Step-by-Step Guidance

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

   

2. Recall that both capacitors store the same charge $Q$.

3. Use the formula for potential energy stored in a capacitor to compare $U_1$ and $U_2$.

4. Analyze which statements (i) and (ii) are supported by the formulas and the effect of the dielectric.

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 than Capacitor 1. For the same charge, the potential energy stored in Capacitor 1 is larger because $U = \frac{Q^2}{2C}$ and $C_1 < C_2$.