Electric Charges and Coulomb's law Quiz 1

 

MCQs – Electric Charges & Coulomb’s Law

Section A: Theory / Conceptual (1–10)

1.

Which of the following statements about electric charge is correct?

A. Charge can be created but not destroyed
B. Charge is always continuous
C. Charge is conserved in isolated systems
D. Charge exists only in positive form

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2.

Two identical conducting spheres carrying charges $q_1$ and $q_2$ are touched and then separated. The charge on each sphere becomes

A. $q_1 + q_2$
B. $\frac{q_1+q_2}{2}$
C. $q_1-q_2$
D. $q_1q_2$

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3.

Coulomb’s law is strictly valid for

A. Large charged bodies
B. Point charges or spherically symmetric charges
C. Conductors only
D. Insulators only

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4.

In the vector form of Coulomb’s law,

$$\vec F = k\frac{q_1 q_2}{r^2}\hat r$$

the unit vector $\hat r$ indicates

A. magnitude of force
B. direction from charge $q_1$ to charge $q_2$
C. direction perpendicular to line joining charges
D. direction of velocity

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5.

If two charges $+q$ and $-q$ are placed at a distance $r$, the force between them will be

A. zero
B. attractive
C. repulsive
D. infinite

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6.

If the distance between two charges is tripled, the electrostatic force becomes

A. $F/3$
B. $F/6$
C. $F/9$
D. $F/27$

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7.

Electric charge is quantized. This means

A. charge is always positive
B. charge exists in discrete units
C. charge is continuous
D. charge cannot move

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8.

The constant $k$ in Coulomb’s law in vacuum is approximately

A. $9 \times 10^9$
B. $9 \times 10^{-9}$
C. $8.85 \times 10^{-12}$
D. $3 \times 10^8$

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9.

Two equal charges placed at a distance exert force $F$. If one charge becomes zero, the force becomes

A. $F$
B. $F/2$
C. zero
D. infinite

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10.

The force between two charges acts along

A. perpendicular to line joining charges
B. line joining the charges
C. circular path
D. random direction

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Section B: Numerical (11–20)

11.

Two charges $2\mu C$ and $3\mu C$ are placed 1 m apart in vacuum.

Force between them is

A. 0.054 N
B. 0.27 N
C. 0.18 N
D. 0.009 N

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12.

Two charges exert a force of 16 N when placed 2 m apart.
Force when distance becomes 4 m

A. 16 N
B. 8 N
C. 4 N
D. 2 N

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13.

Two charges $+5\mu C$ and $+5\mu C$ are placed 2 m apart.
Force between them is approximately

A. 0.56 N
B. 0.28 N
C. 0.11 N
D. 0.05 N

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14.

Two identical metal spheres carry charges $+4C$ and $+2C$.
After touching and separating, each sphere will carry

A. $6C$
B. $3C$
C. $2C$
D. $4C$

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15.

Two charges $q$ and $q$ exert force $F$.
If both charges are doubled, new force becomes

A. $F$
B. $2F$
C. $4F$
D. $8F$

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16.

Two charges exert force 9 N at distance 3 m.
Force at 1 m

A. 9 N
B. 27 N
C. 81 N
D. 3 N

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17.

Two identical conducting spheres have charges $+6C$ and $-2C$.
After touching and separating, charge on each sphere becomes

A. $4C$
B. $2C$
C. $1C$
D. $3C$

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18.

Two charges $q$ and $4q$ are separated by distance $r$.
Force between them is $F$.

If charges become $2q$ and $8q$, the new force becomes

A. $F$
B. $2F$
C. $4F$
D. $8F$

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19.

If the force between two charges becomes 9 times, the distance must become

A. $r/3$
B. $3r$
C. $r/9$
D. $9r$

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20.

Two equal charges are separated by distance $r$.
Force is $F$. If distance becomes $r/2$, the force becomes

A. $F/4$
B. $F/2$
C. $2F$
D. $4F$

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Answer Key

Q	Ans
1	C
2	B
3	B
4	B
5	B
6	C
7	B
8	A
9	C
10	B
11	A
12	C
13	D
14	B
15	C
16	C
17	B
18	C
19	A
20	D

Detailed Solutions

Section A: Theory / Conceptual

1.

Electric charge obeys the law of conservation of charge.

This means the total charge in an isolated system remains constant.

Correct Answer: C

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2.

When two identical conducting spheres touch, charge redistributes equally.

Total charge

$$q_{total}=q_1+q_2$$

Charge on each sphere

$$q=\frac{q_1+q_2}{2}$$

Correct Answer: B

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3.

Coulomb’s law is strictly valid for

• Point charges

• Spherically symmetric charge distributions

Correct Answer: B

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4.

Vector form of Coulomb’s law

$$\vec F = k\frac{q_1q_2}{r^2}\hat r$$

Where

• $\hat r$ is the unit vector from charge $q_1$ to $q_2$

Correct Answer: B

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5.

Charges of opposite sign attract.

$$+q \quad -q$$

Force between them is attractive.

Correct Answer: B

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6.

From Coulomb’s law

$$F = k\frac{q_1 q_2}{r^2}$$

If distance becomes 3r

$$F' = k\frac{q_1 q_2}{(3r)^2}$$ $$F' = \frac{F}{9}$$

Correct Answer: C

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7.

Quantization of charge

$$q = ne$$

where

• $n$ = integer

• $e = 1.6\times10^{-19} C$
  

Thus charge exists in discrete packets.

Correct Answer: B

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8.

Coulomb constant

$$k=\frac{1}{4\pi\epsilon_0}$$

Value

$$k = 9 \times 10^9 \, Nm^2/C^2$$

Correct Answer: A

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9.

Force between charges

$$F=k\frac{q_1q_2}{r^2}$$

If one charge becomes zero

$$F = 0$$

Correct Answer: C

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10.

Electrostatic force acts along the line joining the charges.

Correct Answer: B

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Section B: Numerical

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11.

Given

$$q_1 = 2\mu C = 2\times10^{-6}C$$
$$q_2 = 3\mu C = 3\times10^{-6}C$$
$$r = 1m$$

Coulomb law

$$F = k\frac{q_1q_2}{r^2}$$ $$F = 9\times10^9 \frac{(2\times10^{-6})(3\times10^{-6})}{1}$$ $$F = 9\times10^9 \times 6\times10^{-12}$$
$$F = 54\times10^{-3}$$
$$F = 0.054 N$$

Correct Answer: A

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12.

$$F \propto \frac{1}{r^2}$$

Initial

$$F_1=16N$$
$$r_1=2m$$

Final

$$r_2=4m$$
$$F_2 = F_1\left(\frac{r_1}{r_2}\right)^2$$
$$F_2 = 16\left(\frac{2}{4}\right)^2$$
$$F_2 = 16\times\frac{1}{4}$$ $$F_2=4N$$

Correct Answer: C

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13.

$$q_1=q_2=5\mu C$$
$$r=2m$$
$$F= k\frac{q_1q_2}{r^2}$$ $$F=9\times10^9 \frac{25\times10^{-12}}{4}$$ $$F=9\times6.25\times10^{-3}$$
$$F=56.25\times10^{-3}$$
$$F \approx 0.056N$$

Closest option given is 0.05 N.

Correct Answer: D

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14.

Initial charge

$$4C + 2C = 6C$$

After touching (identical spheres)

$$q = \frac{6}{2} = 3C$$

Correct Answer: B

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15.

Initial force

$$F = k\frac{q^2}{r^2}$$

New charges

$$2q,2q$$
$$F' = k\frac{(2q)(2q)}{r^2}$$ $$F' = k\frac{4q^2}{r^2}$$ $$F' = 4F$$

Correct Answer: C

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16.

$$F \propto \frac{1}{r^2}$$ $$F_1=9N$$
$$r_1=3m$$
$$r_2=1m$$
$$F_2 = F_1\left(\frac{r_1}{r_2}\right)^2$$
$$F_2 = 9(3)^2$$
$$F_2=81N$$

Correct Answer: C

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17.

Total charge

$$6 + (-2) = 4C$$

After touching

$$q = \frac{4}{2}$$ $$q = 2C$$

Correct Answer: B

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18.

Original force

$$F = k\frac{q(4q)}{r^2}$$ $$F = 4k\frac{q^2}{r^2}$$

New charges

$$2q,8q$$
$$F' = k\frac{(2q)(8q)}{r^2}$$ $$F' = 16k\frac{q^2}{r^2}$$ $$F' = 4F$$

Correct Answer: C

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19.

$$F \propto \frac{1}{r^2}$$

Force becomes

$$9F$$

Thus

$$\frac{1}{r'^2} = 9\frac{1}{r^2}$$ $$r' = \frac{r}{3}$$

Correct Answer: A

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20.

Distance becomes

$$r/2$$
$$F' = k\frac{q_1q_2}{(r/2)^2}$$ $$F' = k\frac{q_1q_2}{r^2/4}$$ $$F' = 4F$$

Correct Answer: D