Electrostatics - Electric Potential Solved Examples (Class 12 Physics)
Electrostatics potential numericals cover electric potential, potential difference, and work done by electric fields. These problems are essential for unde
TL;DR: Electrostatics potential numericals cover electric potential, potential difference, and work done by electric fields. These problems are essential for…
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Electrostatics potential numericals cover electric potential, potential difference, and work done by electric fields. These problems are essential for unde
Electrostatics - Electric Potential — Solved Numerical Examples (Step by Step)
Example 1: Calculate the electric potential at a distance of 0.1 m from a point charge of 2 × 10^-6 C. (k = 9 × 10^9 N·m²/C²)
Solution: Charge Q = 2 × 10^-6 C, Distance r = 0.1 m, k = 9 × 10^9 N·m²/C². Electric potential V = kQ/r = (9 × 10^9 × 2 × 10^-6) / 0.1 = (18 × 10^3) / 0.1 = 1.8 × 10^5 V.
Example 2: The electric potential at a point is 100 V. What is the work done to bring a charge of 2 C from infinity to this point?
Solution: Electric potential V = 100 V, Charge q = 2 C. Work done W = q × V = 2 × 100 = 200 J.
Example 3: Two point charges of +3 μC and -3 μC are placed 0.1 m apart. Calculate the potential at the midpoint. (k = 9 × 10^9 N·m²/C²)
Solution: Charge Q₁ = 3 × 10^-6 C, Charge Q₂ = -3 × 10^-6 C, Distance between = 0.1 m. Distance from each to midpoint = 0.05 m. Potential at midpoint = V₁ + V₂ = (9 × 10^9 × 3 × 10^-6) / 0.05 + (9 × 10^9 × (-3 × 10^-6)) / 0.05 = 540,000 - 540,000 = 0 V.
Example 4: A uniform electric field of 100 N/C points in the positive x-direction. Calculate the potential difference between two points 0.5 m apart along the field direction.
Solution: Electric field E = 100 N/C, Distance d = 0.5 m. Potential difference V = E × d = 100 × 0.5 = 50 V.
Example 5: A charge of 5 × 10^-6 C is moved from potential 100 V to 300 V. Calculate the work done by external force.
Solution: Charge q = 5 × 10^-6 C, Initial potential V₁ = 100 V, Final potential V₂ = 300 V. Potential difference ΔV = 300 - 100 = 200 V. Work done by external force W = q × ΔV = 5 × 10^-6 × 200 = 1 × 10^-3 J = 0.001 J.
Tips
- Electric potential V = kQ/r for point charges; it is a scalar quantity.
- Work done = charge × potential difference (W = q × ΔV).
- Potential difference is the work per unit charge.
Frequently Asked Questions
What is the difference between electric field and electric potential?
Electric field is the force per unit charge (vector). Electric potential is the work per unit charge (scalar). Potential difference drives current in circuits.
Why is potential at infinity taken as zero?
By convention, potential approaches zero as distance from a charge approaches infinity. This reference point (zero potential at infinity) simplifies calculations.
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