Electric Potential
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| Electric Potential |
`V = \frac{W}{q_0}`
Here,
W = Work done
`q_0 =` Unit Charge
The S.I. unit of electric potential is volt.
`\text{1 volt} = \frac {\text{1 Joule (J)}}{\text{1 Coulomb (C)}}`
The electric potential at a point is 1 volt when the work done in bringing a 1 Coulomb charge from infinity to that point is 1 Joule.
Dimensional Formula of electric potential
`\text{Electric Potential} = \frac{\text{Work done}}{\text{Unit Charge}}`
`V = \frac{W}{q_0}`
`V = \frac{F S}{q_0}` `(\because W = F S)`
`V = \frac{[M^1L^1T^{-2}][L^1]}{[T^1A^1]}`
`V = \frac{[M^1L^2T^{-2}]}{[T^1A^1]}`
`V = [M^1L^2T^{-3}A^{-1}]`
Important Points
(a) The work is done against electric force.
(b) The work done does depend on the path.
Relationship between electric potential and electric field
`dV = \frac{W}{q_0}` (where, dV = potential difference)
`dV = \frac{F dr}{q_0}` (where, r = displacement)
`dV = \frac{F}{q_0} dr `
`dV = E dr ` (where, E = Electric field intensity)
`E = \frac{dV}{dr}`
Hence,
`1 N/C = 1 V/m`
Unit of Electric field intensity E is `N/C`
Unit of electric potential V is `V/m`
We can also define another unit called electron volt (eV) for energy.
Electric Potential Difference
Equipotential Surface
Properties of an Equipotential Surface
The amount of work that has to be done in bringing a unit positive charge from infinity to a point is called the electric potential of that point.
(or)
The electric potential energy stored in a unit point positive charge located at a point is equal to the electric potential of that point.
MCQs on Electric Potential
1. The electric potential at a point is equal to:
(a) The kinetic energy of a unit positive charge
(b) The work done by an external force
(c) The displacement of a unit positive charge
(d) The magnetic field intensity
2. The SI unit of electric potential is:
(a) Watt (W)
(b) Volt (V)
(c) Coulomb (C)
(d) Ampere (A)
3. The dimensional formula of electric potential is:
(a) ` [M^1L^2T^-3A^-1]`
(b) ` [M^1L^2T^-2A^-1]`
(c) ` [M^-1L^-2T^3A^1]`
(d) ` [M^-1L^-2T^2A^1]`
4. The relationship between electric potential and electric field is given by:
(a) `dV = F/q_0`
(b) `E = (dV)/(dr)`
(c) `V = F/q_0`
(d) `E = F/(dr)`
5. The unit of electric field intensity E is:
(a) V/m
(b) N/C
(c) J/C
(d) `C/m^2`
6. What is the potential difference denoted by ΔV?
(a) The amount of work done in the electric field
(b) The displacement between two points in the electric field
(c) The change in kinetic energy of a charge
(d) The difference in electric potential between two points
7. If the potential at point A is 10 V and the potential at point B is 5 V, what is the potential difference between them?
(a) 15 V
(b) 5 V
(c) -5 V
(d) -10 V
8. Which statement about an equipotential surface is true?
(a) It has a varying electric potential at different points
(b) Work done on the surface is always zero
(c) Electric field lines intersect the surface
(d) It has a uniform zero.
9. How many equipotential surfaces are created by a single point charge?
(a) None
(b) One
(c) Finite number
(d) Infinite number
10. What is the direction of the electric field with respect to an equipotential surface?
(a) Parallel
(b) Perpendicular
(c) Tangential
(d) Radial
Answers:
1. (b) The work done by an external force
2. (b) Volt (V)
3. (a) `[M^1L^2T^-3A^-1]`
4. (b) `E = (dV)/(dr)`
5. (b) N/C
6. (d) The difference in electric potential between two points
7. ((c) -5 V
8. (b) Work done on the surface is always zero
9. (d) Infinite number
10. (b) Perpendicular
Short Answer Type Questions with Answers
1. What is the definition of electric potential?
Answer: The electric potential at a point is equal to the work done by an external force in bringing a unit positive charge from infinity to that point inside the electric field without changing its kinetic energy.
2. How is electric potential denoted?
Answer: Electric potential is denoted by the symbol V.
3. What is the SI unit of electric potential?
Answer: The SI unit of electric potential is the volt (V).
4. Define the dimensional formula of electric potential.
Answer: The dimensional formula of electric potential is `[M^1L^2T^(-3)A^(-1)]`.
5. What is the relationship between electric potential and electric field?
Answer: The relationship between electric potential (V) and electric field (E) is given by the equation E = dV/dr, where dV represents the potential difference and dr represents displacement.
6. What is the unit of electric field intensity (E)?
Answer: The unit of electric field intensity (E) is newton per coulomb (N/C).
7. Define the electric potential difference (ΔV).
Answer: Electric potential difference is the amount of work done to bring a unit charge from one point to another in an electric field. It is denoted by ΔV and its unit is the volt (V).
8. What is an equipotential surface?
Answer: An equipotential surface is a surface in an electric field where the electric potential is the same at all points.
9. State some properties of an equipotential surface.
Answer:
- Infinite equipotential surfaces exist around a point charge.
- A single point charge creates infinite equipotential surfaces around itself.
- The amount of electrical energy is the same at all points on an equipotential surface.
- The electric potential is the same at all points on an equipotential surface.
- Two equipotential surfaces never intersect each other.
- Work done in moving a charge on an equipotential surface is always zero.
- The electric field is perpendicular to the equipotential surface.
10. What is the unit of electric potential in terms of electron volts (eV)?
Answer: One electron volt (eV) is equal to `1.6 \times 10^(-19)` joules (J).
Numerical Questions
1. Two point charges 4 μC and −6 μC are seperated by a distance of 10 cm in air. At what point between the charges on the line joining the charges is the potential zero. (Potential at point 4cm from charge 4μC is zero.)
2. Four charges +3μC,−1μC,+5μC and −7μC are arranged on the circumference of a circle of radius 0.5m. The potential at the centre is `(zero)`
3. Two equipotential surfaces are separated by a distance of 5 cm. If the electric potential difference between them is 10 V, what is the magnitude of the electric field between these surfaces? (200 V/m)
4. A charge of +2 μC is moved from a point at 10 V to another point at 5 V. What is the electric potential difference experienced by the charge? (-5 V)
5. What is the work done in moving a test charge q through a distance of 1 cm along the equatorial axis of an electric dipole? (Zero)
What is Electric Potential difference?
Electric potential difference refers to the amount of work required to move a unit positive charge from one point to another in an electric field, against the electric field. It is a scalar quantity measured in volts (V).
Related Questions
1. Define electric potential.
2. How is electric potential different from electric potential energy?
3. What is the SI unit of electric potential?
4. State the relationship between electric potential and electric field.
5. Explain the concept of equipotential surfaces.
6. What is the equipotential surface?
NCERT CHAPTER 2 PHYSICS CLASS 12
- Electric Potential
- Potential due to a Point Charge
- Electric Potential due to Charged Conducting Sphere with Derivation
- Electric Potential Due to Charged Non-Conducting Sphere
- Electric Potential due to Dipole at any Point
- Equipotential Surfaces and Properties of Equipotential Surface
- Electric Potential Due to a Group of Charges and Relation between Electric Field and Potential
- Electric Potential Energy of a System of Two-Point Charges
- Define the Electrostatic Potential Energy of a System of Two and Three-Point Charges
- Work in Rotation of Electric Dipole in Electric Field
- Potential Energy of a Dipole in an External Field
- Electrostatics of Conductors
- Dielectrics and polarization
- Capacitors and Capacitance, The Parallel Plate Capacitance and Effect of Dielectric on Capacitance
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