Electric Charges and Fields Test

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Electric Charges and Fields Test - 75

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Weekly Quiz Competition

Question 1
1 / -0

Two charges, each equal q, are kept at $$x=-a$$ and $$x=a$$ on the x-axis. A particle of mass $$m$$ and charge $${q_0} = \frac{q}{2}$$ is placed at the origin. If charge $${q_0}$$ is given a small displacement $$(y<<a)$$ along the y-axis, the net force acting on the particle is proportional to:

A
$$y$$

B
$$-y$$

C
$$\frac{1}{y}$$

D
$$-\frac{1}{y}$$

Solution
Question 2
1 / -0

Two insulated, similar copper spheres $$A$$ and $$B$$ are separated by a distance of $$0.5$$ m. Each sphere carries a charge of $$6.5 \times {10^{ - 7}}C$$.
i) What is the force of repulsion between them $$(F_{1})$$?
ii) What will be this force if the distance between them doubled $$(F_{2})$$

A
$$F_{1} = 1.52 \times 10^{-2}N$$, $$F_{2} = 3.80 \times 10^{-3} N$$

B
$$F_{1} = 3.80 \times 10^{-3}N$$, $$F_{2} = 1.52 \times 10^{-2} N$$

C
$$F_{1} = 1.52 \times 10^{-3}N$$, $$F_{2} = 3.80 \times 10^{-2} N$$

D
$$F_{1} = 1.52 \times 10^{-2}N$$, $$F_{2} = 3.80 \times 10^{-2} N$$

Solution
Question 3
1 / -0

Two small identical spheres each of mass $$1\ g$$ and carrying same charge $${10}^{-9}$$ care suspended by threads of equal lengths. If the distance between the centres of the spheres is $$0.3\ cm$$ in equilibrium then the inclination of the thread with the vertical will be:-

A
$${\tan }^{-1}\left (0.1\right)$$

B
$${\tan }^{-1}\left (2\right)$$

C
$${\tan }^{-1}\left (1.5\right)$$

D
$${\tan }^{-1}\left (0.6\right)$$

Solution
Question 4
1 / -0

A point charge $$q=10^{-11}\ C$$, is placed at $$4\ cm$$ above a square plate $$(8\ cm\ \times 8\ cm)$$, having charge density $$0.5\ \times 10^{-8}\ C/m^{2}$$. Find the flux related with it.

A
$$0.188\ V-m$$

B
$$0.12\ V-m$$

C
$$0.288\ V-m$$

D
$$0.388\ V-m$$

Solution
Question 5
1 / -0

The volume charge density as a function of distance $$x$$ from one face inside a unit cube is varying as shown in the figure. Then the total flux $$(in S.I units)$$ through the cube if $$(p-{0}=8085\times10^{-12}Cm^{3})$$ is

A
$$\dfrac{1}{4}$$

B
$$\dfrac{1}{2}$$

C
$$\dfrac{3}{4}$$

D
$$1$$
Question 6
1 / -0

The electric field in a region of space is given by $$E=(5\ \hat {i}+2\hat {j})N/C$$. The electric flux through an area of $$2\ m^{2}$$ lying in the $$YZ$$ plane, in $$S.I.$$. units is ?

A
$$10$$

B
$$20$$

C
$$10\sqrt {2}$$

D
$$2\sqrt {29}$$

Solution
Question 7
1 / -0

A charge q is distributed uniformly on a ring of radius R. A sphere of equal radius R is constructed with its centre at the periphery of the ring, Find the flux of the electric field through the surface of the sphere

A
$$\dfrac{q}{\epsilon_0}$$

B
$$\dfrac{q}{2\epsilon_0}$$

C
$$\dfrac{q}{3\epsilon_0}$$

D
Zero.

Solution

Let point of intersection of ring & sphere are $$P.Q.........$$ let center of ring is $$O$$ & center of sphere is $$O'$$........
$$O O'$$ bisects $$P Q$$ in two equal ,if $$S$$ is the point of intersection of $$O O'$$ & $$P Q$$ then
In triangle right angles $$POS$$
$$PO=R, OS=R/2$$ so angle $$POS=\theta$$
Using trigonometry, $$ cos \theta =OS/PS=1/2$$
$$\theta =\pi/3$$
total angle subtended by arc is $$2 \pi/3.....$$ this is the arc of ring which lies inside sphere & substends
$$2 \pi /3$$ angle at the center of ring.....
for $$2 \pi$$ radian charge =q
for unit radian $$ = \dfrac{q}{{2\pi }}$$
for $$ \dfrac{q}{{2\pi }}$$ radian $${q_1} = \left( {\dfrac{q}{{2\pi }}} \right)\left( {\dfrac{{2\pi }}{3}} \right) = \dfrac{q}{3}$$
total flux through sphere= total charge enclosed $$\dfrac{q}{{3{\varepsilon _0}}}$$
$$\therefore $$ Option $$C$$ is correct.
Question 8
1 / -0

The small spherical balls each carrying a charge $$Q = 10 \mu$$ $$C$$ are suspended by two insulting threads of equal length $$1m$$ each, from a point fixed in the cielling. It is found that is in equilibrium threads are separated by an angle $${60^ \circ}$$ between them, as shown in the figure. What is the tension in the threads (Given : $$\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}Nm/{C^2}$$)

A
$$18N$$

B
$$1.8N$$

C
$$0.18N$$

D
None of these

Solution
Question 9
1 / -0

What is the electric flux linked with closed surface?

A
$$10^{11} Nm^2/C$$

B
$$10^{12} Nm^2/C$$

C
$$10^{10} Nm^2/C$$

D
$$8.85\times10^1{3} Nm^2/C$$

Solution
Question 10
1 / -0

Two point charges placed at a distance 'r' in air exert a force F. The value of distance at which they exerts same force when placed in medium (dielectric constant K) is :-

A
rK

B
r/K

C
$$r/\sqrt{K}$$

D
$$r\sqrt{K}$$

Solution