Electric Charges and Fields Test

Result

Electric Charges and Fields Test - 76

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Weekly Quiz Competition

Question 1
1 / -0

The electric field in a region is given by $$\vec { E } =a\hat { i } +b\hat { j } $$. Here a and b are constants. Find the net flux passing through a square area of side $${ L }_{ 0 }$$ parallel to y-z plane

A
$$a{ L }_{ 0 }^{ 3 }$$

B
$$2a{ L }_{ 0 }^{ 2 }$$

C
$$a{ L }_{ 0 }^{ 2 }$$

D
$$\left( a+b \right) { L }_{ 0 }^{ 2 }$$

Solution
Question 2
1 / -0

Two small spheres each having the charge $$+Q$$ are suspended by insulated threads of length $$L$$
from a hook. This arrangement is taken in space where there is no gravitational effect, then the
angle between the two threads and the tension in each will be :

A
$$180^{\circ}, \dfrac {1}{4\pi \epsilon_{0}} \dfrac {Q^{2}}{(2L)^{2}}$$

B
$$90^{\circ}, \dfrac {1}{4\pi \epsilon_{0}} \dfrac {Q^{2}}{L^{2}}$$

C
$$180^{\circ}, \dfrac {1}{4\pi \epsilon_{0}} \dfrac {Q^{2}}{2L^{2}}$$

D
$$180^{\circ}, \dfrac {1}{4\pi \epsilon_{0}} \dfrac {Q^{2}}{L^{2}}$$

Solution
Question 3
1 / -0

Twelve infinite long wire of uniform linear charge density $$\left( \lambda \right)$$ are passing along the twelve edges of a cube. Find electric flux through any face of cube

A
$$\left( \frac { \lambda l }{2 \varepsilon _{ { 0 } } } \right)$$

B
$$\left( \frac { \lambda l }{ \varepsilon _{ { 0 } } } \right)$$

C
$$\left( \frac { \lambda l }{3 \varepsilon _{ { 0 } } } \right)$$

D
$$\left( \frac { 3\lambda l }{ \varepsilon _{ { 0 } } } \right) $$

Solution
Question 4
1 / -0

A conducting sphere of radius a has charge Q on it. It is enclosed by a neutral conducting concentric concentric spherical shell having inner radius 2a and outer radius 5a. Find electrostatic energy of system.

A
$$\dfrac{5}{12} \dfrac{kQ^2}{a}$$

B
$$\dfrac{11}{12} \dfrac{kQ^2}{a}$$

C
$$]dfrac{kQ^2}{2a}$$

D
$$none$$

Solution
Question 5
1 / -0

A non conducting sphere of radius $$'a'$$ has a type charge $$'+q'$$ uniformly distributed throughout in volume. A hollow spherical conductor having inner and outer, radii $$'b'$$ and $$'c'$$ and net charge $$'-q'$$ is concentric with the sphere (see the figure)
Read the following statements
(i) The electric field at a distance $$r$$ from the center of the sphere $$ = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{qr}}{{{a^3}}}$$ for $$r<a$$.
(ii) The electric field at distance $$r$$ from the center of the sphere for $$a<r<b=0$$
(iii) The electric field at distance $$r$$ from the center of the sphere for $$ b<r<c<=0$$
(iv) The charge on the inner surface of the hollow sphere $$=-q$$
(v) The charge on the outer surface of the hollow sphere $$=+q$$.

A
(i),(ii) and (v)

B
(i),(iii) and (iv)

C
(ii),(iii) and (v)

D
(ii),(iii) and (v)

Solution
Question 6
1 / -0

A non conducting sphere of radius $$'a'$$ has a type charge $$'+q'$$ uniformly distributed throughout in volume. A hollow spherical conductor having inner and outer, radii $$'b'$$ and $$'c'$$ and net charge $$'-q'$$ is concentric with the sphere (see the figure)
Read the following statements
(i) The electric field at a distance $$r$$ from the center of the sphere $$ = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{qr}}{{{a^3}}}$$ for $$r<a$$.
(ii) The electric field at distance $$r$$ from the center of the sphere for $$a<r<b=0$$
(iii) The electric field at distance $$r$$ from the center of the sphere for $$ b<r<c<=0$$
(iv) The charge on the inner surface of the hollow sphere $$=-q$$
(v) The charge on the outer surface of the hollow sphere $$=+q$$.

A
(i),(ii) and (v)

B
(i),(iii) and (iv)

C
(ii),(iii) and (v)

D
(ii),(iii) and (iv)

Solution

Solution
Let $$q^{1}$$ is the inner surface charge.
then, $$q_{outer}= -q-q^{1}$$ such that
$$q_{inner}+q_{outer}= -q$$
Electric field inside
the conductor should
be zero ( r > b and r < e)
so in the arbitrary
Gaussian surface
Electric flux = $$\dfrac{q_{inside}}{\varepsilon _{0}}= 0$$
$$\Rightarrow q_{inside}( b < r < c)= q^{1}+q=0$$
$$q^{1}= -q$$
So, $$q_{inner}= -q$$ and $$q_{outer}=0$$
(i) Electric field for r < a ia,
$$E.4\pi r^{2}= \dfrac{q_{inside}}{\varepsilon _{0}}$$
As a charge is uniformly distributed
q inside = $$(\dfrac{r^{3}}{a^{3}})q$$
So, $$E. 4\pi r^{2}= \dfrac{r^{3}q}{a^{3}\varepsilon _{0}}$$
$$\Rightarrow E= \dfrac{1}{4\pi }\times \dfrac{q}{a^{3}\varepsilon _{0}}$$
(ii) Electric field for a < r < b,
$$E= \dfrac{kq}{r^{2}}$$
(iii) Electric field for b < r < c
As told earlier, E = 0
(iv) Electric field for c < r
$$E= \dfrac{k_{qouter}}{r^{2}}= k\dfrac{(0)^{2}}{r^{2}}=0$$
Option - B is correct.
Question 7
1 / -0

A charge of $$+2\mu C$$ is placed at $$x=0$$ and a charge of $$32\ \mu C$$ at $$x=60\ cm$$. A third charge $$Q$$ is placed on the $$x-$$axis, such that it experiences no force. The distance of the point from $$+2\mu C$$ is (in $$cm$$)

A
$$-20$$

B
$$20$$

C
$$12$$

D
$$10$$

Solution
Question 8
1 / -0

Two points charges $$Q$$ and $$-3Q$$ are placed at some distance apart. If the electric field at the location of $$Q$$ is $$E$$ then at the locality of $$-3Q$$, it is

A
$$-E$$

B
$$E/3$$

C
$$-3E$$

D
$$-E/3$$

Solution
Question 9
1 / -0

Two similar balls of mass 'm' are hung by a silk thread of length L and carry similar charge Q as shown in figure Assuming the separation to be small, the separation between the balls (denoted by x) is equal to

A
$$\left[ \frac { Q ^ { 2 } \cdot 2 L } { 4 \pi \varepsilon _ { 0 } \cdot m g } \right] ^ { \frac { 1 } { 3 } }$$

B
$$QLmg$$

C
$$\frac { Q L } { m g }$$

D
$$\frac { Q ^ { 2 } L } { 2 \pi m g }$$

Solution
Question 10
1 / -0

An inductor having $$400$$ turns, carrying of $$8 m A$$ and inductances $$5 mH$$ then flux is:

A
$$\mu_0$$

B
$$4 \pi/\mu_0$$

C
$$\mu_0/4 \pi$$

D
$$4 \pi$$

Solution