Electric Charges and Fields Test

Result

Electric Charges and Fields Test - 56

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Weekly Quiz Competition

Question 1
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A charged body has an electric flux F associated with it . Now if the body is place inside a conducting shell then the electric flux outside the shell is:

A
zero

B
Greater than F

C
Less than F

D
Equal to F

Solution

A conducting shell does not allow to escape any flux outside, thus confining all fluxes within it.so,flux outside the shell will be zero.
[this happens due to electrostatic sheilding by the conducting shell]
Question 2
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A charge of 1.0C is the placed at the top of the your college building and another equal charge at the top of your house. Take the separation between the two charges to be 2.0 km. Find the force exerted by the charges on each other.

A
$$2.25 \times 10^3$$ N

B
$$2.5 \times 10^3$$ N

C
$$225 \times 10^3$$ N

D
$$2.25 \times 10^5$$ N

Solution

The force of attraction between two charges separated by distance r is given by:
$$F=\dfrac{kq_1q_2}{r^2}$$ (where $$k=\dfrac{1}{4\pi \epsilon_0}=9\times 10^9Nm^2/C^2$$)
$$\Rightarrow F=9\times 10^9\times \dfrac{1\times 1}{2000^2}$$ (separation $$2km=2000$$m)
$$\Rightarrow F=\dfrac{9}{4}\left(\dfrac{10^9}{10^6}\right)=2.25\times 10^3$$N.
Question 3
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Two coaxial coils are very close to each other and their mutual inductance is $$5$$ mH. If a current $$50\sin 500r$$ is passed in one of the coils then the peak value of induced e.m.f. in the secondary coil will be?

A
$$5000$$V

B
$$500$$V

C
$$150$$V

D
$$125$$V

Solution

by the principle of mutual inductance we know that flux induced in coil 2 will depends on the current flowing in coil 1
$$\phi _{ 2 }=Mi_{ 1 }$$
M = mutual inductance
$$i1$$ = current in first coil

now by Faraday's law induced EMF in 2nd coil will be
$$\dfrac { d\phi }{ dt } =EMF$$
$$EMF=M\dfrac { di_{ 1 } }{ dt } $$
now plug in value of current and mutual inductance
$$EMF=5\times 10^{ -3 }\dfrac { d }{ dt } (50sin500t$$
$$EMF=5\times 10^{ -3 }50\times 500\times cos500t$$
$$EMF=125cos500t$$
so above is the equation of induced EMF

so maximum value of induced EMF will be
$$EMF_{ max }=125volts$$
Question 4
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In a region of space, the electric field is given by $$\vec {E} = 8\hat {j} + 4\hat {j} + 3\hat {k}$$. The electric flux through a surface of area of $$100$$ units in $$x - y$$ plane is?

A
$$800\ units$$

B
$$300\ units$$

C
$$400\ units$$

D
$$1500\ units$$

Solution

$$\vec {E} = 8\hat {i} + 4\hat {j} + 3\hat {k}, \vec {A} = 100\hat {k}$$.
Electric flux $$\phi=\vec E\cdot A=(8\hat I+4 \hat j+3\hat k)\cdot 100\hat k=300$$
Question 5
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Determine the ratio $${q}_{1}/{q}_{2}$$. The lines of forces of two point charges are shown in figure.

A
$$ \dfrac { { q }_{ 1 } }{ { q }_{ 2 } } =4$$

B
$$ \dfrac { { q }_{ 1 } }{ { q }_{ 2 } } =3$$

C
$$ \dfrac { { q }_{ 1 } }{ { q }_{ 2 } } =2$$

D
$$ \dfrac { { q }_{ 1 } }{ { q }_{ 2 } } =1$$

Solution
Question 6
1 / -0

There are two charges +2 $$\mu$$ C and -3 $$\mu$$ C. The ratio of forces acting on them will be

A
$$2$$ : $$3$$

B
$$1$$ :$$ 1$$

C
$$3$$ : $$2$$

D
$$4$$ : $$9$$

Solution
Question 7
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A positive charge $${q_o}$$ placed at a point $$P$$ near a charged body experiences a force of repulsion of magnitude $$F$$, the electric field $$E$$ of the charged body at $$P$$ is

A
$$\frac{F}{{{q_0}}}$$

B
$$ < \frac{F}{{{q_0}}}$$

C
$$ > \frac{F}{{{q_0}}}$$

D
$$F$$

Solution
Question 8
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4 charges Q q Q q are placed in the vertices of square ABCD. Find the magnitude of force on charge q at corner C

A
$$\dfrac{KQ}{a^{2}}({\sqrt{2}q + \dfrac{Q}{2}})$$

B
$$\dfrac{KQ}{a^{2}}({\sqrt{4}q + \dfrac{Q}{2}})$$

C
$$\dfrac{KQ}{a^{2}}({\sqrt{3}q + \dfrac{Q}{2}})$$

D
$$\dfrac{KQ}{a^{2}}({\sqrt{6}q + \dfrac{Q}{2}})$$

Solution

Charges are placed in this manner :
Charge at $$C$$ experiences force due to charge at $$A,B$$ and $$C$$.
Let $$AB=a$$.
Force as per Columbus law,
$$F_{1} = F_{2} =\dfrac{KQa}{a^{2}} $$ and, $$F_{3} =\dfrac{kQ^{2}}{(a\sqrt{2}^{2})} = \dfrac{ka^{2}}{2a^{2}}$$
$$\vec {F_{1}} k\ \vec {F_{2}}$$ added up along $$\vec {F_{3}}$$ vectonially .
$$\vec {F}' = F\sqrt{2} = \dfrac{\sqrt{2} KQa}{a^{2} } $$ (due to $$F_{1}$$ and $$F_{2}$$)
So, net force at $$c$$ :-
$$F_{net}= F_{3}+F' =\dfrac{\sqrt{2} k Qa}{a^{2}}+ \dfrac{kQ^{2}}{2a^{2}}=\dfrac{kQ}{a^{2}} \left(\sqrt{2} a+ \dfrac{Q}{2} \right)$$
Question 9
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Three equal charges $$2 \times 10^{-6}C$$ each, are held fixed at three vertices of equilateral triangle of side $$5 \,cm$$. The force experienced by one of the charge due to the rest of two is

A
$$22.94 \,N$$

B
$$21.94 \,N$$

C
$$23.94 \,N$$

D
$$24.94 \,N$$

Solution
Question 10
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An infinite cylinder of radius 'R' carrying charge density . $$ p = ar +br^{2}$$ where 'r' distance of point from the axis and a b are non-zero constant. Find the ratio of a/b if field out of the cylinder is zero

A
$$\frac{R}{4}$$

B
-$$\frac{R}{4}$$

C
-$$\frac{3R}{4}$$

D
$$\frac{3R}{4}$$

Solution