Coulombs Law and Electric Field - Exam Prep Insights

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Coulombs Law and Electric Field - Capacitance and Dielectrics

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Coulombs Law and Electric Field - Capacitance and Dielectrics MCQ & Objective Questions

Coulombs Law and Electric Field, along with Capacitance and Dielectrics, are fundamental concepts in physics that play a crucial role in various school and competitive exams. Mastering these topics not only enhances your understanding but also boosts your confidence in tackling objective questions. Practicing MCQs and important questions related to these concepts can significantly improve your exam preparation and scoring potential.

What You Will Practise Here

Understanding Coulombs Law and its applications in electrostatics.
Exploring the concept of electric fields and their graphical representation.
Defining capacitance and its significance in electrical circuits.
Examining the role of dielectrics in capacitors and their effect on capacitance.
Learning key formulas related to Coulombs Law, electric fields, and capacitance.
Solving numerical problems involving electric field strength and capacitance calculations.
Interpreting diagrams related to electric field lines and capacitor configurations.

Exam Relevance

The topics of Coulombs Law, Electric Field, Capacitance, and Dielectrics are frequently featured in CBSE, State Boards, NEET, and JEE exams. Students can expect questions that test their understanding of concepts, as well as numerical problems that require application of formulas. Common patterns include direct application of Coulombs Law, calculating electric field strength, and analyzing capacitor behavior in different scenarios.

Common Mistakes Students Make

Confusing the direction of electric field lines and the force on positive and negative charges.
Misapplying the formula for capacitance, especially when dielectrics are involved.
Overlooking the effect of distance on the strength of electric fields.
Failing to interpret diagrams correctly, leading to errors in understanding field configurations.

FAQs

Question: What is Coulombs Law?
Answer: Coulombs Law states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Question: How does a dielectric affect capacitance?
Answer: A dielectric increases the capacitance of a capacitor by reducing the electric field within the capacitor, allowing it to store more charge for the same voltage.

Now is the time to enhance your understanding of these essential topics! Dive into our practice MCQs and test your knowledge on Coulombs Law and Electric Field - Capacitance and Dielectrics. Your success in exams is just a question away!

Q. If a capacitor of 10 µF is charged to 20 V, what is the energy stored in the capacitor?

A. 0.02 J
B. 0.1 J
C. 0.5 J
D. 0.1 mJ

Solution

Energy stored, U = 0.5 * C * V^2 = 0.5 * 10 x 10^-6 F * (20 V)^2 = 0.02 J.

Correct Answer: B — 0.1 J

Q. If a capacitor of 10 µF is connected in series with a 20 µF capacitor, what is the total capacitance?

A. 6.67 µF
B. 30 µF
C. 15 µF
D. 8 µF

Solution

1/C_total = 1/C1 + 1/C2 = 1/10 + 1/20 = 3/20, thus C_total = 20/3 µF = 6.67 µF.

Correct Answer: A — 6.67 µF

Q. If a dielectric material with a dielectric constant of 4 is placed in a capacitor, how does it affect the capacitance?

A. It halves the capacitance
B. It doubles the capacitance
C. It quadruples the capacitance
D. It does not affect the capacitance

Solution

The capacitance increases by the factor of the dielectric constant, so C' = k * C, where k = 4.

Correct Answer: B — It doubles the capacitance

Q. If a resistor of 10 Ω is connected in series with a 20 Ω resistor, what is the total resistance?

A. 10 Ω
B. 20 Ω
C. 30 Ω
D. 15 Ω

Solution

R_total = R1 + R2 = 10 Ω + 20 Ω = 30 Ω.

Correct Answer: C — 30 Ω

Q. In a circuit with a 12 V battery and a 4 Ω resistor, what is the current flowing through the circuit?

A. 3 A
B. 2 A
C. 4 A
D. 1 A

Solution

Using Ohm's law, I = V/R = 12 V / 4 Ω = 3 A.

Correct Answer: B — 2 A

Q. In a series circuit with a 12 V battery and two resistors of 3 Ω and 6 Ω, what is the current flowing through the circuit?

A. 1 A
B. 2 A
C. 3 A
D. 4 A

Solution

Total resistance R_total = R1 + R2 = 3 Ω + 6 Ω = 9 Ω. Current I = V/R_total = 12 V / 9 Ω = 1.33 A, approximately 1 A.

Correct Answer: B — 2 A

Q. What is the capacitance of a capacitor with a charge of 12 µC and a voltage of 6 V?

A. 2 µF
B. 4 µF
C. 6 µF
D. 8 µF

Solution

C = Q/V = 12 x 10^-6 C / 6 V = 2 x 10^-6 F = 2 µF.

Correct Answer: B — 4 µF

Q. What is the capacitance of a capacitor with a charge of 6 µC and a voltage of 12 V?

A. 0.5 µF
B. 0.25 µF
C. 0.75 µF
D. 1 µF

Solution

C = Q/V = 6 x 10^-6 C / 12 V = 0.5 x 10^-6 F = 0.5 µF.

Correct Answer: A — 0.5 µF

Q. What is the capacitance of a parallel plate capacitor with an area of 0.01 m² and a separation of 0.001 m, filled with a dielectric of k=5?

A. 5.5 µF
B. 5.0 µF
C. 4.5 µF
D. 6.0 µF

Solution

C = k * ε0 * (A/d) = 5 * (8.85 x 10^-12 F/m) * (0.01 m² / 0.001 m) = 5.0 µF.

Correct Answer: B — 5.0 µF

Q. What is the capacitance of a parallel plate capacitor with an area of 0.01 m² and a separation of 0.001 m, filled with a dielectric of k=2?

A. 5.5 µF
B. 4.4 µF
C. 2.2 µF
D. 1.1 µF

Solution

C = k * ε₀ * (A/d) = 2 * (8.85 x 10^-12 F/m) * (0.01 m² / 0.001 m) = 4.4 µF.

Correct Answer: B — 4.4 µF

Q. What is the current through a 5 Ω resistor connected to a 15 V battery?

A. 3 A
B. 2 A
C. 1 A
D. 0.5 A

Solution

Using Ohm's law, I = V/R = 15 V / 5 Ω = 3 A.

Correct Answer: B — 2 A

Q. What is the electric field strength at a distance of 2 m from a point charge of +5 µC?

A. 1.12 N/C
B. 0.56 N/C
C. 2.25 N/C
D. 0.75 N/C

Solution

E = k * |q| / r^2 = (8.99 x 10^9 N m²/C²) * (5 x 10^-6 C) / (2 m)^2 = 1.12 N/C.

Correct Answer: A — 1.12 N/C

Q. What is the electric potential at a point 1 m away from a charge of +1 µC?

A. 9 kV
B. 1 kV
C. 0.9 kV
D. 0.1 kV

Solution

V = k * q / r = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C) / 1 m = 8.99 kV.

Correct Answer: A — 9 kV

Q. What is the electric potential at a point 1 m away from a charge of +3 µC?

A. 9 V
B. 27 V
C. 18 V
D. 36 V

Solution

V = k * q / r = (8.99 x 10^9 N m²/C²) * (3 x 10^-6 C) / (1 m) = 26.97 V, approximately 27 V.

Correct Answer: B — 27 V

Q. What is the electric potential at a point 3 m away from a charge of +1 µC?

A. 3000 V
B. 9000 V
C. 300 V
D. 900 V

Solution

V = k * q / r = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C) / 3 m = 3000 V.

Correct Answer: C — 300 V

Q. What is the electric potential energy stored in a capacitor of 2 µF charged to 12 V?

A. 0.144 mJ
B. 0.288 mJ
C. 0.576 mJ
D. 0.072 mJ

Solution

U = 1/2 * C * V² = 1/2 * 2 x 10^-6 F * (12 V)² = 0.144 mJ.

Correct Answer: B — 0.288 mJ

Q. What is the energy stored in a capacitor of 5 µF charged to a voltage of 10 V?

A. 0.25 mJ
B. 0.5 mJ
C. 0.75 mJ
D. 1 mJ

Solution

Energy (U) = 0.5 * C * V² = 0.5 * 5 x 10^-6 F * (10 V)² = 0.25 mJ.

Correct Answer: A — 0.25 mJ

Q. What is the equivalent capacitance of two capacitors, 4 µF and 6 µF, connected in series?

A. 2.4 µF
B. 10 µF
C. 1.5 µF
D. 3.6 µF

Solution

1/C_eq = 1/C1 + 1/C2 = 1/4 + 1/6 => C_eq = 2.4 µF.

Correct Answer: A — 2.4 µF

Q. What is the equivalent resistance of three resistors of 2 Ω, 3 Ω, and 5 Ω connected in series?

A. 10 Ω
B. 5 Ω
C. 8 Ω
D. 12 Ω

Solution

R_total = R1 + R2 + R3 = 2 Ω + 3 Ω + 5 Ω = 10 Ω.

Correct Answer: A — 10 Ω

Q. What is the equivalent resistance of three resistors of 2 Ω, 3 Ω, and 5 Ω in series?

A. 10 Ω
B. 8 Ω
C. 5 Ω
D. 3 Ω

Solution

R_eq = R1 + R2 + R3 = 2 Ω + 3 Ω + 5 Ω = 10 Ω.

Correct Answer: A — 10 Ω

Q. What is the equivalent resistance of two resistors, 4 Ω and 6 Ω, connected in parallel?

A. 2.4 Ω
B. 10 Ω
C. 24 Ω
D. 1.5 Ω

Solution

1/R_total = 1/R1 + 1/R2 = 1/4 + 1/6 = 5/12, thus R_total = 12/5 Ω = 2.4 Ω.

Correct Answer: A — 2.4 Ω

Q. What is the force between two charges of +1 µC and +1 µC separated by 0.1 m?

A. 0.09 N
B. 0.18 N
C. 0.02 N
D. 0.04 N

Solution

F = k * |q1 * q2| / r² = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C)² / (0.1 m)² = 0.09 N.

Correct Answer: B — 0.18 N

Q. What is the force between two charges of +1 µC and +1 µC separated by 1 m?

A. 8.99 N
B. 0.009 N
C. 0.089 N
D. 0.899 N

Solution

F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * (1 x 10^-6 C)² / (1 m)² = 8.99 N.

Correct Answer: A — 8.99 N

Q. What is the force between two point charges of +2 µC and -3 µC separated by a distance of 0.5 m?

A. 1.2 N
B. 0.24 N
C. 0.48 N
D. 0.96 N

Solution

Using Coulomb's law, F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * |(2 x 10^-6 C) * (-3 x 10^-6 C)| / (0.5 m)^2 = 0.24 N.

Correct Answer: B — 0.24 N

Q. What is the force between two point charges of +2 µC and -3 µC separated by a distance of 0.5 m in a vacuum?

A. -1.08 N
B. -0.72 N
C. 1.08 N
D. 0.72 N

Solution

Using Coulomb's law, F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * |(2 x 10^-6 C) * (-3 x 10^-6 C)| / (0.5 m)^2 = -1.08 N.

Correct Answer: A — -1.08 N

Q. What is the force between two point charges of +3 µC and -2 µC separated by a distance of 0.5 m?

A. 1.2 N
B. 0.6 N
C. 0.4 N
D. 0.8 N

Solution

Using Coulomb's law, F = k * |q1 * q2| / r^2 = (8.99 x 10^9 N m²/C²) * |3 x 10^-6 C * -2 x 10^-6 C| / (0.5 m)² = 1.2 N.

Correct Answer: A — 1.2 N

Q. What is the force on a charge of +1 µC placed in an electric field of 1000 N/C?

A. 0.001 N
B. 0.1 N
C. 1 N
D. 10 N

Solution

F = q * E = (1 x 10^-6 C) * (1000 N/C) = 0.001 N.

Correct Answer: B — 0.1 N

Q. What is the force on a charge of +1 µC placed in an electric field of 500 N/C?

A. 0.5 N
B. 1 N
C. 2 N
D. 0.2 N

Solution

F = q * E = (1 x 10^-6 C) * (500 N/C) = 0.5 N.

Correct Answer: A — 0.5 N

Q. What is the potential difference across a 5 µF capacitor charged to 10 V?

A. 50 mJ
B. 0.05 J
C. 0.5 J
D. 5 J

Solution

Energy stored in a capacitor, U = 0.5 * C * V^2 = 0.5 * (5 x 10^-6 F) * (10 V)^2 = 0.05 J.

Correct Answer: B — 0.05 J

Q. What is the potential difference across a capacitor of 5 µF charged to 10 V?

A. 0.05 V
B. 0.5 V
C. 5 V
D. 50 V

Solution

V = Q/C; Q = C * V = 5 µF * 10 V = 50 µC, thus the potential difference is 10 V.

Correct Answer: C — 5 V

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