Electric charge, Coulomb's law and superposition — practice questions

Question 1 · difficulty L2 · understanding

Two point charges $\mathrm{q}_1=3 \mu C$ and $\mathrm{q}_2=-4 \mu C$ are placed at points $(2 \hat{i}+3 \hat{j}+3 \hat{k})$ and $(\hat{i}+\hat{j}+\hat{k})$ respectively. Force on charge $\mathrm{q}_2$ is $\_\_\_\_$ N. (Take $\frac{1}{4 \pi \epsilon_0}=9 \times 10^9$ SI Units)

• A. $(12 \hat{i}+24 \hat{j}+24 \hat{k}) \times 10^{-3}$
• B. $(4 \hat{i}+8 \hat{j}+8 \hat{k}) \times 10^{-3}$
• C. $(3 \hat{i}+6 \hat{j}+6 \hat{k}) \times 10^{-3}$
• D. $(-4 \hat{i}-8 \hat{j}-8 \hat{k}) \times 10^{-3}$

Question 2 · difficulty L2 · understanding

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4 \times 10^{-8} \mathrm{C}$ charge and then removed to a distance such that the force of repulsion between them is $9 \times 10^{-3} \mathrm{~N}$. The distance between them is (Take $\frac{1}{4 \pi \epsilon_{\mathrm{o}}}$ as $9 \times 10^9$ in SI units)

• A. 1 cm
• B. 2 cm
• C. 4 cm
• D. 3 cm

Question 3 · difficulty L2 · understanding

Two charged conducting spheres of radii $$a$$ and $$b$$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

• A. $$a b$$
• B. $$\frac{b}{a}$$
• C. $$\frac{a}{b}$$
• D. $$\sqrt{a b}$$

Question 4 · difficulty L2 · understanding

The vehicles carrying inflammable fluids usually have metallic chains touching the ground:

• A. To protect tyres from catching dirt from ground
• B. It is a custom
• C. To alert other vehicles
• D. To conduct excess charge due to air friction to ground and prevent sparking

Question 5 · difficulty L2 · understanding

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

• A. 10 19
• B. 10 39
• C. 10 29
• D. 10 36

Question 6 · difficulty L2 · understanding

Force between two point charges $$q_1$$ and $$q_2$$ placed in vacuum at '$$r$$' cm apart is $$F$$. Force between them when placed in a medium having dielectric constant $$K=5$$ at '$$r / 5$$' $$\mathrm{cm}$$ apart will be:

• A. $$5 F$$
• B. $$25 F$$
• C. $$F / 5$$
• D. $$F / 25$$

Question 7 · difficulty L2 · understanding

If two charges q$$_1$$ and q$$_2$$ are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?

• A. $$d\sqrt k$$
• B. $$1\,.\,5d\sqrt k$$
• C. $$k\sqrt d$$
• D. $$2d\sqrt k$$

Question 8 · difficulty L2 · understanding

A charge of $$4 \,\mu \mathrm{C}$$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be :

• A. $$1 \,\mu \mathrm{C}$$ and $$3 \,\mu\mathrm{C}$$
• B. $$2 \,\mu \mathrm{C}$$ and $$2\, \mu \mathrm{C}$$
• C. 0 and $$4\, \mu\, \mathrm{C}$$
• D. $$1.5 \,\mu \mathrm{C}$$ and $$2.5\, \mu \mathrm{C}$$

Question 9 · difficulty L2 · understanding

Two identical charged particles each having a mass 10 g and charge 2.0 $$\times$$ 10 $$-$$7 C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 ms $$-$$2 ]

• A. 12 cm
• B. 10 cm
• C. 8 cm
• D. 5 cm

Question 10 · difficulty L2 · understanding

A point charge $$q_1=4q_0$$ is placed at origin. Another point charge $$q_2=-q_0$$ is placed at $$x=12$$ cm. Charge of proton is $$q_0$$. The proton is placed on $$x$$ axis so that the electrostatic force on the proton is zero. In this situation, the position of the proton from the origin is ___________ cm.