Electrostatic force – problems and solutions

1. If the static electric force is 144 N, what is the distance between both charges… (1 μC = 10^{-6 }C and k = 9.10^{9} N.m^{2}.C^{-2})

__Known :__

Electric force (F_{12}) = 144 N

Charge 1 (q_{1}) = 10 μC = 10 x 10^{-6 }C

Charge 2 (q_{2}) = 4 μC = 4 x 10^{-6 }C

Constant (k) = 9 x 10^{9} N.m^{2}.C^{-2}

*C = Coulomb, N = Newton, m = meter*

__Wanted :__ Distance between both charges (r)

__Solution :__

The equation of Coulomb’s law :

*F = the static electric force, k = **Coulomb’s constant, q = electric charge, r = distance between both charges*

Distance between both charges (r) = 5 x 10^{-2} meter = 5 x 10^{-2} x 10^{2 }cm = 5 cm.

2. Two charges separated by a distance of r. If the static electric force is 3.6 N, what is the distance between both charges (1 μC = 10^{-6 }C and k = 9.10^{9} N.m^{2}.C^{-2})

__Known :__

Electric force (F_{12}) = 3.6 N

Charge 1 (q_{1}) = 9 μC = 9 x 10^{-6 }C

Charge 2 (q_{2}) = 4 μC = 4 x 10^{-6 }C

Coulomb’s constant (k) = 9 x 10^{9} N.m^{2}.C^{-2}

*C = Coulomb, N = Newton, m = meter*

__Wanted :__ Distance between both charges (r)

__Solution :__

Distance between both charges (r) = 0.3 m = 0.3 x 100 cm = 30 cm.

3. Three point charges as shown in figure below. What is the magnitude of the static electric force at point A (k = 9.10^{9} N.m^{2}.C^{-2}; 1 μ = 10^{-6})

__Known :__

Charge A (q_{A}) = -2 μC = -2 x 10^{-6 }C

Charge B (q_{B}) = 8 μC = 8 x 10^{-6 }C

Charge C (q_{C}) = 4,5 μC = 4,5 x 10^{-6 }C

Coulomb‘s constant (k) = 9 x 10^{9} N.m^{2}.C^{-2}

Distance between charge A and B (r_{AB}) = 4 cm = 4 x 10^{-2} m

Distance between charge A and C (r_{AC}) = 3 cm = 3 x 10^{-2} m

*C = Coulomb, N = Newton, m = meter*

__Wanted :__ The static electric force at point A

__Solution :__

The equation of Coulomb’s law :

*F = **the static electric force**, k = **Coulomb**‘s constant**, q = **electric charge**, r = **distance between both charges*

The static electric force at point A :

4. Three-point charges as shown in the figure below. What is the magnitude of Coulomb force experienced by Charge B (k = 9.10^{9} N.m^{2}.C^{-2}; 1 μC = 10^{-6 }C).

Known :

q_{A} = 10 µC = 10 x 10^{-6} C = 10^{-5} Coulomb

q_{B} = 10 µC = 10 x 10^{-6} = 10^{-5} Coulomb

q_{C} = 20 µC = 20 x 10^{-6} = 2 x 10^{-5} Coulomb

r_{AB} = 0.1 meter = 10^{-1} m

r_{BC} = 0.1 meter = 10^{-1} m

k = 9 x 10^{9} Nm^{2}C^{−2}

__Wanted :__ Coulomb force experienced by Charge B

__Solution :__

There are two coulomb forces act on charge B, Coulomb force between charge A and B (F_{AB}) and Coulomb force between charge B and C (F_{BC}). Coulomb force experienced by charge B is net force of F_{AB} and F_{BC}.

__Coulomb force between charge A and B :__

Charge A signed positive and charge B signed positive so that F_{AB} points to charge C.

__Coulomb force between charge B and C :__

Charge B signed positive and charge C signed positive so that F_{BC} points to charge A.

__Coulomb force experienced by charge B :__

F_{B} = F_{BC }– F_{AB} = 180 – 90 = 90 N

Coulomb force experienced by charge B (F_{B}) is 90 Newton. The direction of F_{B} same as the direction of F_{BC }points to charge A.

5. Determine the magnitude and direction of Coulomb force on charge B (k = 9 x 10^{9} Nm^{2}C^{−2}, 1 μC = 10^{−6} C).

__Known :__

Charge A (q_{A}) = +Q

Charge B (q_{B}) = -2Q

Charge C (q_{C}) = -Q

Distance between charge A and B (r_{AB}) = r

Distance between charge B and C (r_{BC}) = 2r

k = 9 x 10^{9} Nm^{2}C^{−2}

__Wanted :__ Magnitude and direction of Coulomb force on charge B

__Solution :__

Coulomb force between charge A and B :

Charge A positive and charge B negative so that the direction of F_{AB }points to charge A.

Coulomb force between charge B and charge C :

Charge B is negative and charge C is negative so that the direction of F_{BC }points to charge A.

Net force act on charge B :

F = F_{AB} + F_{BC }= 2 k Q^{2}/r^{2} + 0.5 k Q^{2}/r^{2} = 2.5 k Q^{2}/r^{2} = 2.5 k Q^{2} r^{-2}

Direction of force points to charge A or to leftward.