Question

Derive an expression for electrostatic potential energy of system of n point charges

Answer 1

Answer:

V = k × [q/r]

V = electric potential energy, q = point charge, r = distance between any point around the charge to the point charge, k = Coulomb constant; k = 9.0 × 109 N.

General Formula: Voltage = Energy / charge

SI Unit: Volt

Denoted by: V, ∆V, U, ∆U

Dimension: ML2T-3A-1

The electric potential energy of a system of point charges is defined as the work required assembling this system of charges by bringing them close together, as in the system from an infinite distance. ... is the electric potential generated by the charges, which is a function of position r.

To have a physical quantity that is independent of test charge, we define electric potential V (or simply potential, since electric is understood) to be the potential energy per unit charge V=PEq V = PE q .

The potential difference between points A and B, VB − VA, defined to be the change in potential energy of a charge q moved from A to B, is equal to the change in potential energy divided by the charge, Potential difference is commonly called voltage, represented by the symbol ΔV: ΔV=ΔPEq Δ V = Δ PE q and ΔPE = qΔV.

The equation for the electric potential due to a point charge is V=kQr V = kQ r , where k is a constant equal to 9.0×109 N⋅m2/C2.

Explanation:

mrk me as BRAINLIEST

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Answer 2

The electrostatic potential energy of a system of n point charges can be derived using the concept of work done in moving a charge from infinity to a certain position in the presence of other charges.

• Consider a system of n point charges q1, q2, q3, ..., qn. Let the potential energy of the system be U. Now, let's take a small charge q0, and bring it from infinity to a certain position r in the presence of the other charges. The work done in bringing q0 to position r is given by:
• dW = F.dr
• Where F is the electrostatic force acting on q0 due to the other charges, and dr is the displacement of q0.
• The electrostatic force F is given by Coulomb's law:
• F = (1/4πε) * (q0 * q1 / r1^2 + q0 * q2 / r2^2 + ... + q0 * qn / rn^2)
• Where ε is the permittivity of the medium, ri is the distance between q0 and qi, and qi is the charge of the ith point charge.
• Substituting the expression for F in the equation for work done, we get:
• dW = (1/4πε) * q0 * (q1 / r1^2 + q2 / r2^2 + ... + qn / rn^2) * dr
• The total work done in bringing q0 from infinity to the position r is obtained by integrating the above expression from infinity to r:
• W = ∫∞r (1/4πε) * q0 * (q1 / r1^2 + q2 / r2^2 + ... + qn / rn^2) * dr
• The electrostatic potential energy U of the system is defined as the work done in bringing all the point charges to their respective positions from infinity, which is given by:
• U = W = ∫∞r (1/4πε) * q0 * (q1 / r1^2 + q2 / r2^2 + ... + qn / rn^2) * dr
• Now, we can replace q0 with any of the points charges q1, q2, ..., qn, and sum up the potential energies of all the charges to get the total electrostatic potential energy of the system:
• U = (1/2) * Σi=1n Σj≠i^n (1/4πε) * qi * qj / rij
• where rij is the distance between charges qi and qj.
• Therefore, the electrostatic potential energy of a system of n point charges can be expressed as the sum of the potential energies of all the pairs of charges in the system.

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