UK K12 GCSE/A-Level: Year 12 A-Level Lower Sixth Physics - Electric Fields, Coulomb's Law, Capacitors

Learning Objectives

By the end of this topic, students will be able to:

• Explain Coulomb's Law and its application to electric fields
• Describe the concept of capacitance and the factors affecting it
• Calculate the capacitance of a capacitor in series and parallel configurations
• Analyze the behavior of capacitors in different circuit configurations
• Evaluate the role of capacitors in filtering and energy storage

Core Concepts

Coulomb's Law states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, this is expressed as:

F = k * (q1 * q2) / r^2

where F is the force, k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.

The concept of electric field is closely related to Coulomb's Law. An electric field is a region around a charged particle where the force on other charges can be detected. The electric field strength is defined as the force per unit charge:

E = F / q

Capacitors are devices that store electric energy in the form of an electric field. A capacitor consists of two conductive plates separated by an insulating material called a dielectric. When a voltage is applied across the capacitor, an electric field is created between the plates, and the capacitor begins to store energy.

The capacitance of a capacitor is defined as the ratio of the charge stored to the voltage applied:

C = Q / V

The capacitance of a capacitor depends on the area of the plates, the distance between them, and the dielectric constant of the material between them.

Worked Examples

Example 1: Coulomb's Law

Two point charges of 2 ?C and 3 ?C are separated by a distance of 0.5 m. Calculate the force between them.

Using Coulomb's Law, we can calculate the force as:

F = k * (q1 * q2) / r^2 = 9 * 10^9 * (2 * 10^-6 * 3 * 10^-6) / (0.5)^2 = 0.216 N

Example 2: Capacitance

A capacitor has a capacitance of 10 ?F and is charged to a voltage of 5 V. Calculate the charge stored on the capacitor.

Using the formula for capacitance, we can calculate the charge as:

Q = C * V = 10 * 10^-6 * 5 = 50 ?C

Example 3: Capacitor in Series

Two capacitors of 20 ?F and 30 ?F are connected in series. Calculate the equivalent capacitance.

The reciprocal of the equivalent capacitance is the sum of the reciprocals of the individual capacitances:

1/C_eq = 1/20 + 1/30 C_eq = 12 ?F

Common Misconceptions

• Many students mistakenly believe that the electric field strength is proportional to the distance between the charges. In fact, it is inversely proportional to the square of the distance.
• Some students may think that the capacitance of a capacitor is independent of the voltage applied. However, the capacitance is actually a function of the voltage, as the dielectric constant of the material between the plates can change with voltage.
• Students may also believe that a capacitor can store an infinite amount of energy. However, the energy stored in a capacitor is limited by the voltage and capacitance of the device.

Exam Tips

• Make sure to use the correct units for all calculations, including Coulomb's constant and the distance between charges.
• When calculating the capacitance of a capacitor, remember to use the formula C = Q / V.
• In questions involving capacitors in series or parallel, make sure to use the correct formula for the equivalent capacitance.
• When evaluating the behavior of capacitors in different circuit configurations, consider the effects of the capacitor on the circuit's voltage and current.

MCQs with Explanations

MCQ 1: Coulomb's Law [F]

What is the force between two point charges of 2 ?C and 3 ?C separated by a distance of 0.5 m?

A) 0.1 N B) 0.216 N C) 2 N D) 10 N

Correct answer: B) 0.216 N

Why the distractors fail:

• A) This answer is too small, as the force is proportional to the product of the charges.
• C) This answer is too large, as the force is inversely proportional to the square of the distance.
• D) This answer is much too large, as the force is proportional to the product of the charges and inversely proportional to the square of the distance.

MCQ 2: Capacitance [H]

A capacitor has a capacitance of 10 ?F and is charged to a voltage of 5 V. What is the charge stored on the capacitor?

A) 20 ?C B) 50 ?C C) 100 ?C D) 200 ?C

Correct answer: B) 50 ?C

Why the distractors fail:

• A) This answer is too small, as the charge is proportional to the capacitance and voltage.
• C) This answer is too large, as the charge is proportional to the capacitance and voltage.
• D) This answer is much too large, as the charge is proportional to the capacitance and voltage.

MCQ 3: Capacitor in Series [H]

Two capacitors of 20 ?F and 30 ?F are connected in series. What is the equivalent capacitance?

A) 10 ?F B) 12 ?F C) 20 ?F D) 30 ?F

Correct answer: B) 12 ?F

Why the distractors fail:

• A) This answer is too small, as the equivalent capacitance is the sum of the reciprocals of the individual capacitances.
• C) This answer is too large, as the equivalent capacitance is the sum of the reciprocals of the individual capacitances.
• D) This answer is the larger of the two individual capacitances, but not the equivalent capacitance.

MCQ 4: Electric Field [F]

What is the unit of electric field strength?

A) N/C B) V/m C) A/s D) W/m^2

Correct answer: A) N/C

Why the distractors fail:

• B) This answer is the unit of electric potential difference, not electric field strength.
• C) This answer is the unit of current, not electric field strength.
• D) This answer is the unit of power density, not electric field strength.

MCQ 5: Capacitor in Parallel [H]

Two capacitors of 20 ?F and 30 ?F are connected in parallel. What is the equivalent capacitance?

A) 10 ?F B) 20 ?F C) 30 ?F D) 50 ?F

Correct answer: D) 50 ?F

Why the distractors fail:

• A) This answer is too small, as the equivalent capacitance is the sum of the individual capacitances.
• B) This answer is too small, as the equivalent capacitance is the sum of the individual capacitances.
• C) This answer is too small, as the equivalent capacitance is the sum of the individual capacitances.

Short-answer Questions

1. Describe the concept of electric field and its relationship to Coulomb's Law.

(Answer should include a clear explanation of electric field and its definition, as well as its relationship to Coulomb's Law.)

1. A capacitor has a capacitance of 10 ?F and is charged to a voltage of 5 V. Calculate the energy stored in the capacitor.

(Answer should include a clear calculation of the energy stored using the formula for energy, including the correct units.)

1. Two capacitors of 20 ?F and 30 ?F are connected in series. Calculate the equivalent capacitance and explain why it is the correct formula.

(Answer should include a clear calculation of the equivalent capacitance using the correct formula, as well as an explanation of why this formula is used.)

1. Describe the behavior of a capacitor in a circuit with a voltage source and a resistor.

(Answer should include a clear explanation of how the capacitor affects the circuit, including the effects on voltage and current.)

1. A capacitor has a capacitance of 10 ?F and is connected in parallel with a resistor of 100 ?. Calculate the time constant of the circuit and explain its significance.

(Answer should include a clear calculation of the time constant using the correct formula, as well as an explanation of its significance in the context of the circuit.)