Static electricity – problems and solutions

Electric force

1. Point A in an electric field. The magnitude of the electric field at point A = 0.5 NC-1. If a 0.25-C charge placed at point A, then what is the electric force exerted on the charge.

Known :

Electric field at point A = 0.5 NC-1

Electric charge at point A = 0.25 C

Wanted: Electric force

Solution :

F = q E

F = (0.25 C)(0.5 NC-1)

F = 0.125 N

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2. Two charges 5 C and 4 C are separated by a distance of 3 meters. If Coulomb constant is 9 × 109 Nm2 C–2, what is the magnitude of electric force experienced by two charges?

Known :

Charge 1 (q1) = 5 C

Charge 2 (q2) = 4 C

Distance between charge 1 and charge 2 (r) = 3 meters

Coulomb’s constant (k) = 9 × 109 Nm2 C–2

Wanted : The magnitude of the electric force (F)

Solution :

Static electricity – problems and solutions 1

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3. Electric charge +q1 = 10 μC ; +q2 = 20 μC ; and q3 are separated, as shown in figure below. The electric force exerted on charge q2 = 0, then what is the charge of q3.

Static electricity – problems and solutions 2

Known :

Charge 1 (q1) = 10 μC = 10 x 10-6 C

Charge 2 (q2) = 20 μC = 20 x 10-6 C

Wanted : What is the charge of q3

Solution :

There are two forces acts on +q2.

The first force is the repulsive force between charge +q1 and charge +q2 that is F12, rightward.

The net electric force acts on q2 = 0 then q3 must negative.

The second force is the attractive force between charge +q2 and -q3 that is F23, leftward.

Both of these forces act on q2, have the same magnitude but the opposite direction.

Static electricity – problems and solutions 3

Net force acts on +q2 = 0.

Static electricity – problems and solutions 4

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4. Three charges q1, q, and q2 are in a line. If q = 5.0 μC and d = 30 cm, then what is the magnitude and direction of the electric force acts on the charge q.

Static electricity – problems and solutions 5

Known :

Charge 1 (q1) = 30 μC = 30 x 10-6 C

Charge 2 (q2) = 60 μC = 60 x 10-6 C

Charge 3 (q) = 5 μC = 5 x 10-6 C

Distance between q1 and q = d

Distance between q2 and q = 2d

d = 30 cm = 0.3 meters

d2 = (0.3)2 = 0.09

Coulomb’s constant (k) = 9 x 109 N m2 C-2

Wanted : The magnitude and the direction of the electric force acts on the electric charge

Solution :

There are two forces act on q that is F1 rightward (q and q1 are positive so F1 away from q and q1) and F2 leftward (q and q2 are positive so F2 away from q and q2). First calculated F1 and F2.

Static electricity – problems and solutions 6The net force is 7.5 Newton. The direction of the net force = the direction of F1, rightward point to charge q2.

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Electric field

5. A point charge q is at the point P in the electric field produced by the charge (+) so that it experiences a force of 0.05 N in the direction towards the charge. If the magnitude of the electric field at point P is 2 x 10-2 NC-1, then what is the magnitude and type of charge that causes the electric field.

Known :

Electric force (F) = 0.05 N

Electric field (E) = 2 x 10 –2 NC –1 = 0.02 NC –1

Wanted: The magnitude and type of electric charge

Solution :

The electric charge is calculated using a formula that expresses the relationship between electric force (F), the electric field (E) and electric charge (q):

F = q E

q = F / E = 0.05 N / 0.02 NC –1 = 2.5 Coulomb

The charge q experiences an electric force in the direction to charge (+) which produces an electric field, so the charge q is negative.

6. Charge A and B are separated by a distance of 4 meters. Point C is between both charges, 1 meter from point A. If QA = –300 μC, QB = 600 μC. 1/4 π ε0 = 9 × 109 N m2 C– 2, then what is the magnitude of the electric field at point C produced by both charges.

Known :

Distance between charge A and B (rAB) = 4 meters

Distance between point C and charge A (rAC) = 1 meter

Distance between point C and charge B (rBC) = 3 meters

Charge A (qA) = –300 μC = -300 x 10-6 C = -3 x 10-4 Coulomb

Charge B (qB) = 600 μC = 600 x 10-6 C = 6 x 10-4 Coulomb

Constant (k) = 9 × 109 N m2 C–2

Wanted : Electric field at point C

Solution :

Electric field produced by charge A at point C :

Static electricity – problems and solutions 7

Charge A is negative so that the direction of the electric field point to charge A and away from charge B (to left).

The electric field produced by charge B on point C :

Static electricity – problems and solutions 8

Charge B is positive so that the direction of electric field away from charge B and point to charge A (to left).

The resultant of the electric field at point A :

E = EA + EB

E = (27 x 105) + (6 x 105)

E = 33 x 105 N/C

The direction of the electric field point to charge A and away from charge B (to left).

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7. A 1-mg dust float in the air. If the charge of the dust is 0.5 μC and acceleration due to gravity is 10 m/s2, determine the magnitude of the electric field that supports dust.

Known :

Mass of dust (m) = 1 mg = 1 x 10-6 kg

Charge of dust (q) = 0.5 μC = 0.5 x 10-6 C

Acceleration due to gravity (g) = 10 m/s2

Wanted : Electric field

Solution :

w = m g

w = weight of dust, m = mass of dust, g = acceleration due to gravity

The force of gravity acts on dust :

w = m g = (1 x 10-6 kg)(10 m/s2) = 10 x 10-6 kg m/s2 = 10 x 10-6 Newton

The equation of the electric field :

E = F/q

E = electric field, F = electric force, q = electric charge

Substitute F in the equation of electric field with w in the equation of weight :

E = F/q = w/q

E = (10 x 10-6 N) / (0.5 x 10-6 C)

E = 10 N / 0,5 C

E = 20 N/C

8. Two charges q1 = 32 μC and q2 = -214 μC are separated by a distance of x, as shown in figure below. No electric field at point P located at 10 cm from q2. Find x.

Static electricity – problems and solutions 9

Known :

Charge 1 (Q1) = 32 μC

Charge 2 (Q2) = -214 μC

Distance of point P from q1 = x + 10 cm

The distance of point P from q2 = 10 cm

Wanted: x

Solution :

Static electricity – problems and solutions 10

E1 = electric field produced by charge Q1. The direction of the electric field away from Q1 because Q1 is positive. E2 = electric field produced by Q2. The direction of the electric field point to Q2 because Q2 is negative.

No net force at point p located at 10 cm from Q2

Static electricity – problems and solutions 11

Use quadratic formula :

Static electricity – problems and solutions 12

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9. A charged point q is at the point P in the electric field produced by the charge (+), thus having a force of 0.05 N. If the charge is +5 × l0–6 Coulomb, then what is the magnitude of the electric field at point C.

Known :

Electric force (F) = 0.05 Newton

Electric charge (Q) = +5 × l0–6 Coulomb = 0.000005

Wanted : Electric field at point P

Solution :

E = F / Q

E = 0.05 Newton / 0.000005 Coulomb

E = 5 Newton / 0.0005 Coulomb

E = 10,000 Newton/Coulomb

E = 104 N/C

E = 104 NC-1