Electric Charges and Fields Test

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Electric Charges and Fields Test - 82

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Question 1
1 / -0

Force $$F$$ between charges $$Q_{1}$$ and $$Q_{2}$$ separated by $$r$$ is $$25\ N$$. It can be reduced to $$5\ N$$ if the separation between them is made.

A
$$r/\sqrt {5}$$

B
$$r/2$$

C
$$2r$$

D
$$\sqrt {5}r$$

Solution
Question 2
1 / -0

The electric field of a plane polarized electromagnetic Wave in free space at time t = 0 i given by an expression
$$\vec{E} (x,y) = 10\hat{j} cos [(6x + 8z)]$$
The magenetic field $$\vec{B}$$ (x,z,t) is given by ; (c is the velocity of light will be:

A
$$\dfrac{1}{c}(4 \hat{k} + 8 \hat{i}) cos [(2x - 8z + 20ct)]$$

B
$$\dfrac{1}{c}(6 \hat{k} - 8 \hat{i}) cos [(6x + 8z - 10ct)]$$

C
$$\dfrac{1}{c}(5 \hat{k} + 8 \hat{i}) cos [(6x + 8z - 80ct)]$$

D
$$\dfrac{1}{c}(4 \hat{k} - 8 \hat{i}) cos [(6x + 8z + 70ct)]$$

Solution

$$\overset{\rightarrow} E = 10\hat{j} cos [(6 \hat{i} + 8 \hat{k}). (x\hat{i} + z\hat{k})]$$
$$= 10 \hat{j} cos [\overrightarrow{K}.\overrightarrow{r}]$$
$$\overrightarrow{K} = 6\hat{i} + 8\hat{K}$$ ; direction of waves travel. i.e direction of 'c'
Direction of $$\hat{B}$$ will be along
$$\hat{C} \times \hat{E} = \dfrac{-4\hat{i} + 3\hat{k}}{5}$$
Mag. of $$\vec{B} = \dfrac{E}{C} = \dfrac{10}{C}$$
$$\therefore \overrightarrow{B} = \dfrac{10}{C}\left(\dfrac{-4\hat{i} + 3\hat{k}}{5}\right) = \dfrac{(-8\hat{i} + 6\hat{k})}{c}$$
Question 3
1 / -0

Two spheres have equal and opposite charges and are at a distance of $$90\, cm$$ from each other. They are touched together and then are placed at their initial position; Then they show a repulsive force of $$0.025\, N$$. The final charge on them will be

A
1.5 μC

B
2 μC

C
3 μC

D
5 μC

Solution
Question 4
1 / -0

There is an electric field of $$100N/C$$ X-direction . the flux passing through a square of 10 cm sides placed on XY plane inside the electric field is _____ $$ Nm^2/C. $$

A
$$0$$

B
$$10$$

C
$$1$$

D
$$2$$

Solution
Question 5
1 / -0

A positive charge particle is released in electric field in case $$(a)$$ it is just released and in case $$(b)$$ it has initial speed $$v_0$$ along electric field. If after sometime its kinetic energy in case $$(a)$$ and $$(b)$$ are $$k_1$$, and $$k_2$$ then

A
$$k_1>k_2$$

B
$$k_1 < k_2$$

C
$$k_1=k_2$$

D
None of these

Solution
Question 6
1 / -0

An observer moves past an electron at rest. His instrument measures :

A
an electric field only

B
a magnetic field only

C
both fields

D
any of the two fields, depending upon his speed.

Solution
Question 7
1 / -0

A loop of area $$4 m ^ { 2 }$$ is placed flat in the x -y plane. There is a constant magnetic field $$ 4 \hat { j }$$ in the region. Find the flux through the loop

A
2 units

B
4 units

C
6 units

D
0 units

Solution
Question 8
1 / -0

A small sphere of mass $$m$$ and having charge $$q$$ is suspended by a silk thread of length $$l$$ in a uniform horizontal electric filed. If it stands at a distance x from the vertical line from point of suspension, then magnitude of electric field is :

A
$$\dfrac{mg}{q}$$

B
$$\dfrac{mg}{q} \dfrac{x}{l}$$

C
$$\dfrac{mg x}{q\sqrt{l^2 - x^2}}$$

D
$$\dfrac{mg l}{q \sqrt{x^2 - l^2}}$$

Solution

$$E=?$$
the distance $$=\sqrt { { l }^{ 2 }-{ x }^{ 2 } } $$
$${ E }_{ q }\sqrt { { l }^{ 2 }-{ x }^{ 2 } } =mgx$$
where $$mg$$ is equivalent to $$E$$
now,
or, $$E=\dfrac { mgx }{ q\sqrt { { l }^{ 2 }-{ x }^{ 2 } } } $$
Question 9
1 / -0

Two infinite linear charges are placed parallel to each other at a distance 0.3 m from each other. If the linear charges density in each is 5 $$\mu C/m$$, then the force acting on a unit length of each linear charge will be :-

A
1.5 N/m

B
3.25 N/m

C
4.5 N/m

D
7.5 N/m

Solution
Question 10
1 / -0

A charge $$q$$ is placed in the middle of a line joining the two equal and like point charges $$Q$$. This system will remain in equilibrium for which the value of $$q$$ is:

A
$$+ \mathrm { Q } / 2$$

B
$$- \mathrm { Q } / 4$$

C
$$+ \mathrm { Q } / 4$$

D
$$- \mathrm { Q } / 2$$

Solution