# 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 10^{9} Nm^{2}C^{−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 10^{9} Nm^{2}C^{−2}

__Wanted :__ Electric potential (V)

__Solution :__

Electric potential :

Electric potential is 4.5 x 10^{6 }Volt

2. Charge Q_{1} = 5.0 μC and charge Q_{2} = 6.0 μC. Coulomb’s constant (k) = 9 x 10^{9} Nm^{2}C^{−2}, 1 μC = 10^{−6} C. Point A located between the charges. Determine electric potential at point A.

__Known :__

Charge Q_{1} = -5.0 μC = -5.0 x 10^{-6} C

The distance of point A from Q_{1} = 10 cm = 0.1 m = 10^{-1 }m

Charge Q_{2} = 6.0 μC = 6.0 x 10^{-6} C

The distance of point a from Q_{2} = 10 cm = 0.1 m = 10^{-1 }m

Coulomb’s constant (k) = 9 x 10^{9} Nm^{2}C^{−2}

__Wanted :__ Electric potential at point A

__Solution :__

Electric potential 1 :

Electric potential 2 :

Electric potential at point A :

V = V_{2 }– V_{1}

V = (54 – 45) x 10^{4}

V = 9 x 10^{4 }

3. Charge q_{1} = 5.0 μC and charge q_{2} = 6.0 μC. Coulomb’s constant (k) = 9 x 10^{9} Nm^{2}C^{−2}, 1 μC = 10^{−6} C. Determine the electric potential at point A.

__Known :__

Charge Q_{1} = -5.0 μC = -5.0 x 10^{-6} C

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

Charge Q_{2} = 6.0 μC = 6.0 x 10^{-6} C

The distance of point A from Q_{2} = 50 cm = 0.5 m = 5 x 10^{-1 }m

Coulomb’s constant (k) = 9 x 10^{9} Nm^{2}C^{−2}

__Wanted :__ Electric potential at point A

__Solution :__

Electric potential 1 :

Electric potential 2 :

Electric potential at point A :

V = V_{1 }+ V_{2}

V = (-11.25 + 10.8) x 10^{4}

V = -0.45 x 10^{4 }

V = -4.5 x 10^{3 }

Electric potential at point A is -4.5 x 10^{3 }Volt