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Chapter Analysis
Advanced31 pages • EnglishQuick Summary
This chapter on Electrostatic Potential and Capacitance deals with concepts such as electrostatic potential energy, potential due to a point charge, and potential energy in an external field. It introduces key principles like the superposition principle for potentials and explains how capacitors function, including their energy storage and the impact of dielectrics. The chapter also covers the relation between electric field and potential and explores the concept of equipotential surfaces.
Key Topics
- •Electrostatic potential energy
- •Potential due to a point charge
- •Capacitors and capacitance
- •Electric field and potential relation
- •Equipotential surfaces
- •Superposition principle for potentials
- •Effect of dielectric materials on capacitance
Learning Objectives
- ✓Understand the concept of electrostatic potential energy and how it is calculated.
- ✓Calculate the potential due to various charge configurations using the superposition principle.
- ✓Describe the functioning and significance of capacitors in storing electrical energy.
- ✓Explain the relationship between electric field strength and potential.
- ✓Understand the role of dielectric materials in modifying capacitance.
- ✓Analyze the concept and properties of equipotential surfaces.
Questions in Chapter
Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
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A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.
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Two charges 2 mC and –2 mC are placed at points A and B 6 cm apart. (a) Identify an equipotential surface of the system. (b) What is the direction of the electric field at every point on this surface?
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A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?
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A parallel plate capacitor with air between the plates has a capacitance of 8 pF (1pF = 10–12 F). What will be the capacitance if the distance between the plates is reduced by half, and the space between them is filled with a substance of dielectric constant 6?
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Three capacitors each of capacitance 9 pF are connected in series. (a) What is the total capacitance of the combination? (b) What is the potential difference across each capacitor if the combination is connected to a 120 V supply?
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Three capacitors of capacitances 2 pF, 3 pF and 4 pF are connected in parallel. (a) What is the total capacitance of the combination?
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Additional Practice Questions
Explain the concept of electric potential energy in an external field.
mediumAnswer: The electric potential energy of a charge in an external electric field is the work done to bring the charge from infinity to that point without acceleration. The potential energy is given by U = qV, where q is the charge and V is the external potential at that point.
How does the presence of a dielectric material affect the capacitance of a capacitor?
hardAnswer: A dielectric material increases the capacitance of a capacitor by reducing the effective electric field within it. This happens because the dielectric becomes polarised, reducing the potential difference for the same charge on the capacitor plates, thereby increasing capacitance. The new capacitance is C = KC_0, where C_0 is the original capacitance and K is the dielectric constant.
Derive the expression for the potential due to a point charge.
hardAnswer: The potential V at a distance r from a point charge Q is given by V = Q / (4πε_0 r), where ε_0 is the permittivity of free space. This is derived by calculating the work done in bringing a unit positive test charge from infinity to a distance r from the charge Q.
What is the superposition principle for potentials?
easyAnswer: The superposition principle states that the total potential at a point due to multiple charges is the algebraic sum of the potentials due to each individual charge. This principle is crucial for calculating potentials in systems with multiple charges.
What is meant by an equipotential surface, and what are its properties?
mediumAnswer: An equipotential surface is a surface on which the electric potential is the same at every point. No work is required to move a charge along an equipotential surface, and the electric field is always perpendicular to this surface.