Electric Charges and Fields Test

Result

Electric Charges and Fields Test - 73

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Question 1
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Electric field at a distance $$4R$$ from the surface of a charge cylinder is $$E$$ . If $$R$$ is the radius of the cylinder and $$L$$ is the length of the cylinder then surface charge density of the cylinder is:

A
$$ \dfrac { 4 \epsilon E }{L} $$

B
$$ \dfrac { 5 \epsilon E }{L} $$

C
$$5 \epsilon E$$

D
$$4 \epsilon E$$

Solution
Question 2
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The net electric force on a charge of $$+3\mu C$$ at the mid-point on the line joining two charges of magnitude $$+2\mu C$$ and $$-2\mu C$$ separated by the distance of $$6\ mm$$, is

A
$$6000\ N$$

B
$$12000\ N$$

C
$$60\ N$$

D
$$zero$$

Solution
Question 3
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Two isolated charge metallic spheres of radii $$R_{1}$$ and $$R_{2}$$ having charge $$Q_{1}$$ and $$Q_{2}$$ respectively are connected to each other, then there is:

A
No charge in the electrical energy of the system

B
An increase in the electrical energy of the system

C
A increase in the electrical energy of the system in any case

D
A decrease in electrical energy of the system if $$Q_{1}R_{2}\neq Q_{2}R_{1}$$

Solution
Question 4
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The electric field at point $$(30,30,0)cm$$ due to a charge of $$0.008\mu C$$ at origin will be _____

A
$$8000N{C}^{-1}$$

B
$$4000(i+j)N{C}^{-1}$$

C
$$200\sqrt{2}(i+j)N{C}^{-1}$$

D
$$400\sqrt{2}(i+j)N{C}^{-1}$$

Solution
Question 5
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Two identical charged spheres suspended from a common point by two mass less strings of lengths l, are initially at a distance d apart because of their mutual repulsion. the charges begin to leak from both the spheres at a constant rate. as a result, the spheres approach each other with the velocity v. then v varies as a function of distance x between the spheres , as

A
$$v$$ directly proportional to $$x^{-1}$$

B
$$v$$ directly proportional to $$x^{1/2}$$

C
$$v$$ directly proportional to $$ x$$

D
$$v $$ directly proportional to $$ x^{-1/2}$$

Solution
Question 6
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A square loop of side b is rotating with angular speed $$\omega$$ about one of the diagonals as axis. At $$t=0$$, the plane of the loop is perpendicular to the magnetic field B. If the number of turns of the loop be N then what is the instantaneous flux through the coil

A
BAN

B
BAN $$sin \omega t$$

C
BAN $$cos \omega t$$

D
BAN $$ \omega t$$

Solution
Question 7
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The potential difference between two isolated spheres of radii $$r_{1}$$ and $$r_{2}$$ is zero. The ratio of their charges $$Q_{1}/Q_{2}$$ will be-

A
$$r_{1}/r_{2}$$

B
$$r_{2}/r_{1}$$

C
$$r_{1}^{2}/r_{2}^{2}$$

D
$$r_{1}^{3}/r_{2}^{3}$$

Solution
Question 8
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An elementary particle of mass $$m$$ and charge $$+e$$ is projected with velocity $$v$$ at a much more massive particle of charge $$Ze$$, where $$Z>0$$. What is the closed possible approach of the incident particle?

A
$$\dfrac{Ze^{2}}{\ 2\pi \varepsilon _{0}mv^{2}}$$

B
$$\dfrac{Ze^{2}}{4\pi \varepsilon _{0}r_{n}}$$

C
$$\dfrac{Ze^{2}}{\ 8\pi \varepsilon _{0}r_{n}}$$

D
$$\dfrac{Ze^{2}}{\ 16\pi \varepsilon _{0}r_{n}}$$

Solution
Question 9
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Two charges each of $$2$$ micro coulomb are $$0.5\ m$$ apart. If both of them axis vacuum, them the force between them is

A
$$1.89\ N$$

B
$$2.44\ N$$

C
$$0.144\ N$$

D
$$3.144\ N$$

Solution
Question 10
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The force of attraction between two charges separated by certain distance in air is $$F_{1}$$. If the space between the charges is completely filled with dielectric of constant $$4$$ the force becomes $$F_{2}$$. If half of the distance between the charges is filled with same dielectric the force between the charges is $$F_{3}$$. Then $$F_{1} : F_{2} : F_{3}$$ is

A
$$16 : 9 : 4$$

B
$$9 : 36 : 16$$

C
$$4 : 1 : 2$$

D
$$36 : 9 : 16$$

Solution