The work required to bring a unit positive charge from...

The work required to bring a unit positive charge from infinity to a mid-point between two charges $20 \mu \mathrm{C}$ and $10 \mu \mathrm{C}$ separated by a distance of $50 \mathrm{~m}$, is : (a) $10.8 \times 10^{4} \mathrm{~J}$ (b) $10.8 \times 10^{3} \mathrm{~J}$ (c) $1.08 \times 10^{6} \mathrm{~J}$ (d) $0.54 \times 10^{5} \mathrm{~J}$

The work required to bring a unit positive charge from infinity to a mid-point between two charges $20 \mu \mathrm{C}$ and $10 \mu \mathrm{C}$ separated by a distance of $50 \mathrm{~m}$, is :
(a) $10.8 \times 10^{4} \mathrm{~J}$
(b) $10.8 \times 10^{3} \mathrm{~J}$
(c) $1.08 \times 10^{6} \mathrm{~J}$
(d) $0.54 \times 10^{5} \mathrm{~J}$

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Key Concepts

Electric Potential

Electric potential is a measure of the potential energy per unit charge at a point in a field. It is determined by the charges creating the field and decreases with distance from those charges. This concept is essential for calculating the work done in moving a charge within an electric field.

Work in Electrostatics

The work done in moving a charge within an electric field is defined as the change in electric potential energy. For a unit charge brought from infinity to a specific point, the work is numerically equal to the electric potential at that point. This concept links the idea of energy conservation to the behavior of charges in an electric field.

Superposition Principle

In electrostatics, the superposition principle states that the total electric potential at a point due to multiple sources is the algebraic sum of the individual potentials produced by each source. This principle simplifies the analysis, allowing one to study complex systems by considering each charge separately.

Coulomb's Law

Coulomb's Law describes the force between two point charges, which is inversely proportional to the square of the distance between them. It also provides a basis for deriving the expression for electric potential from a point charge, linking the concepts of force and energy in an electrostatic field.

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