Electric voltage – problems and solutions

1. Determine the electric potential at a point located at 1 cm from a charge 5.0 μC. Coulomb constant (k) = 9 x 10⁹ Nm²C⁻², 1 μC = 10⁻⁶ C.

Known :

The distance from charge (r) = 1 cm = 1/100 m = 0.01 m = 10^-2 m

Charge (q) = 5.0 μC = 5.0 x 10^-6 C

Coulomb constant (k) = 9 x 10⁹ Nm²C⁻²

Wanted : Electric potential (V)

Solution :

Electric potential :

Electric potential is 4.5 x 10⁶ Volt

2. Charge Q₁ = 5.0 μC and charge Q₂ = 6.0 μC. Coulomb’s constant (k) = 9 x 10⁹ Nm²C⁻², 1 μC = 10⁻⁶ C. Point A located between the charges. Determine electric potential at point A.

Known :

Charge Q₁ = -5.0 μC = -5.0 x 10^-6 C

The distance of point A from Q₁ = 10 cm = 0.1 m = 10^-1 m

Charge Q₂ = 6.0 μC = 6.0 x 10^-6 C

The distance of point a from Q₂ = 10 cm = 0.1 m = 10^-1 m

Coulomb’s constant (k) = 9 x 10⁹ Nm²C⁻²

Wanted : Electric potential at point A

Solution :

Electric potential 1 :

Electric potential 2 :

Electric potential at point A :

V = V₂ – V₁

V = (54 – 45) x 10⁴

V = 9 x 10⁴

3. Charge q₁ = 5.0 μC and charge q₂ = 6.0 μC. Coulomb’s constant (k) = 9 x 10⁹ Nm²C⁻², 1 μC = 10⁻⁶ C. Determine the electric potential at point A.

Known :

Charge Q₁ = -5.0 μC = -5.0 x 10^-6 C

The distance of point A from Q₁ = 40 cm = 0.4 m = 4 x 10^-1 m

Charge Q₂ = 6.0 μC = 6.0 x 10^-6 C

The distance of point A from Q₂ = 50 cm = 0.5 m = 5 x 10^-1 m

Coulomb’s constant (k) = 9 x 10⁹ Nm²C⁻²

Wanted : Electric potential at point A

Solution :

Electric potential 1 :

Electric potential 2 :

Electric potential at point A :

V = V₁ + V₂

V = (-11.25 + 10.8) x 10⁴

V = -0.45 x 10⁴

V = -4.5 x 10³

Electric potential at point A is -4.5 x 10³ Volt