Potential Due To Different Charge Distributions - Calculation Of Potential Due To A Charged Conducting Sphere

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Topic: Potential Due To Different Charge Distributions
Calculation of Potential due to a charged conducting sphere

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Electric potential is defined as the amount of work done in bringing a unit positive charge from infinity to the point in question.
It is calculated using the formula: V = k(Q/r), where V is the electric potential, k is the electrostatic constant, Q is the charge, and r is the distance.

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The potential due to a charged conducting sphere is given by: V = (kQ)/(2R), where V is the potential, Q is the charge on the sphere, R is the radius of the sphere, and k is the electrostatic constant.

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The potential due to a charged conducting sphere is independent of the location of the point within or outside the sphere.
The potential is constant throughout the interior of the sphere, and it is equal to the potential on the surface of the sphere.

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A conducting sphere with a positive charge will have a positive potential.
A conducting sphere with a negative charge will have a negative potential.

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Example: Calculate the potential due to a uniformly charged conducting sphere with a charge of 6 μC and a radius of 2 cm.
Solution: Using the formula V = (kQ)/(2R),
- V = (9 x 10^9 Nm^2/C^2)(6 x 10^-6 C) / (2 x 0.02 m)
- V = 13.5 x 10^6 V

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The electric field due to a charged conducting sphere is given by: E = (kQ)/(R^2), where E is the electric field, Q is the charge on the sphere, R is the radius of the sphere, and k is the electrostatic constant.

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The electric field inside a conducting sphere is zero.
The electric field is non-zero only outside the sphere.

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The potential due to a charged conducting shell is constant throughout the interior and exterior of the shell.
The potential inside the shell is equal to the potential on its surface.

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The potential due to a charged conducting shell is given by: V = (kQ)/R, where V is the potential, Q is the charge on the shell, R is the radius of the shell, and k is the electrostatic constant.

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An electric dipole is formed by two equal and opposite charges separated by a small distance.
The dipole moment (p) is defined as the product of the magnitude of one of the charges and the separation between the charges.
The equation for the dipole moment is given as: p = q * d, where p is the dipole moment, q is the magnitude of the charge, and d is the distance between the charges.

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The potential due to an electric dipole at any point in space is given by: V = (kp * cosθ)/r^2, where V is the potential, kp is the electrostatic constant times the dipole moment, θ is the angle between the dipole axis and the line joining the point to the dipole, and r is the distance between the point and the dipole.

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The electric field due to an electric dipole at any point in space is given by: E = (kp * sinθ)/(r^2), where E is the electric field, kp is the electrostatic constant times the dipole moment, θ is the angle between the dipole axis and the line joining the point to the dipole, and r is the distance between the point and the dipole.

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The potential energy of a dipole in an electric field is given by the equation: U = -p * E, where U is the potential energy, p is the dipole moment, and E is the electric field.

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The torque experienced by a dipole in an electric field is given by the equation: τ = p * E * sinθ, where τ is the torque, p is the dipole moment, E is the electric field, and θ is the angle between the dipole moment and the electric field direction.

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When a dipole is placed in a uniform electric field, it experiences a net force and aligns itself with the field.
The net force experienced by a dipole in an electric field is given by the equation: F = p * dE/dx, where F is the net force, p is the dipole moment, dE/dx is the gradient of the electric field along the x-axis, and d is the separation between the charges.

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Example: Calculate the electric potential at a point P located at a distance of 3 cm from an electric dipole of dipole moment 5 Cm.
Solution: Using the equation V = (kp * cosθ)/r^2,
- V = (9 x 10^9 Nm^2/C^2)(5 Cm * cos(0))/(0.03 m)^2
- V = 1.5 x 10^6 V

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The electric field due to a uniformly charged infinite line of charge is given by: E = (2kλ)/(r), where E is the electric field, k is the electrostatic constant, λ is the linear charge density, and r is the distance from the line of charge.

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The potential due to a uniformly charged infinite line of charge is given by: V = (2kλ)/(r), where V is the potential, k is the electrostatic constant, λ is the linear charge density, and r is the distance from the line of charge.

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The electric field due to a uniformly charged infinite plane sheet of charge is given by: E = (σ)/(2ε₀), where E is the electric field, σ is the surface charge density, and ε₀ is the electric constant.

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Summary of the topic so far:
- Calculation of potential due to a charged conducting sphere
- Potential is independent of location within or outside the sphere
- Electric field is zero inside the sphere, non-zero outside

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Potential due to a point charge: V = (kQ)/r
Potential due to a uniformly charged conducting sphere: V = (kQ)/(2R)
Potential due to a charged conducting shell: V = (kQ)/R

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Electric field due to a charged conducting sphere: E = (kQ)/(R^2)
Electric field is zero inside the sphere and non-zero outside

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Potential due to an electric dipole: V = (kp * cosθ)/r^2
Electric field due to an electric dipole: E = (kp * sinθ)/(r^2)

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Electric field due to a uniformly charged infinite line of charge: E = (2kλ)/(r)
Potential due to a uniformly charged infinite line of charge: V = (2kλ)/(r)

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Electric field due to a uniformly charged infinite plane sheet of charge: E = (σ)/(2ε₀)
Calculate the electric field at a point P located at a distance r from the sheet of charge using the formula

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Summary of the formulas discussed in the lecture:
- Potential due to a charged conducting sphere: V = (kQ)/(2R)
- Potential due to a charged conducting shell: V = (kQ)/R
- Electric field due to a charged conducting sphere: E = (kQ)/(R^2)
- Electric field due to a charged conducting shell: E = (kQ)/(R^2) for points outside the shell

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Summary of the formulas discussed in the lecture (contd.):
- Potential due to an electric dipole: V = (kp * cosθ)/r^2
- Electric field due to an electric dipole: E = (kp * sinθ)/(r^2)
- Electric field due to a uniformly charged infinite line of charge: E = (2kλ)/(r)
- Potential due to a uniformly charged infinite line of charge: V = (2kλ)/(r)

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Summary of the formulas discussed in the lecture (contd.):
- Electric field due to a uniformly charged infinite plane sheet of charge: E = (σ)/(2ε₀)
- Calculation of potential and electric field at different points with relevant formulas

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Important concepts covered in this lecture:
- Calculation of potential and electric field for different charge distributions
- Potential due to charged conducting sphere and shell
- Electric field due to charged conducting sphere and shell, as well as a dipole, infinite line of charge, and infinite plane sheet of charge.