Electric Charges and Fields Test

Result

Electric Charges and Fields Test - 84

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Weekly Quiz Competition

Question 1
1 / -0

A charged water drop whose radius is $$ 0.1\mu m$$ is in equilibrium in an electric field. If charge on it is equal to charge of an electron, then intensity of electric field will be $$(g = 10 { m }^{ -1 }$$)

A
$$1.61 N/C$$

B
$$26.2 N/C$$

C
$$262 N/C$$

D
$$1610 N/C$$

Solution
Question 2
1 / -0

An electron and a proton are in a uniform electric field, the ratio of their accelerations will be

A
Zero

B
Unity

C
The ratio of the masses of proton and electron in order

D
The ratio of the masses of electron and proton

Solution
Question 3
1 / -0

The total flux associated with the given cube will be where $$'a'$$ is side of the cube:-
$$\left(\dfrac{1}{\epsilon_0} = 4\pi \times 9 \times 10^{9}\ SI\ units\right)$$

A
$$162\pi \times 10^{-3} Nm^{2}/C$$

B
$$162\pi \times 10^{3} Nm^{2}/C$$

C
$$162\pi \times 10^{-6} Nm^{2}/C$$

D
$$162\pi \times 10^{6} Nm^{2}/C$$

Solution
Question 4
1 / -0

Identify the wrong statement in the following:
Coulomb's law correctly describes the electric force that

A
Binds the electrons of an atom to its nucleus

B
Binds the protons and neutrons in the nucleus of an atom

C
Binds atoms together to form molecules

D
Binds atoms and molecules together to form solids
Question 5
1 / -0

Equal charges q are placed at the vertices A and B of an aquilateral triangle ABC of side a. The magnitude of electric field at the point C due to two charges is.

A
$$\frac { a }{ 4\pi { \epsilon }_{ 0 }{ a }^{ 2 } } $$

B
$$\frac { \sqrt { 2q } }{ 4\pi { \epsilon }_{ 0 }{ a }^{ 2 } } $$

C
$$\frac { \sqrt { 3q } }{ 4\pi { \epsilon }_{ 0 }{ a }^{ 2 } }$$

D
$$\frac { q }{ 4\pi { \epsilon }_{ 0 }{ a }^{ 2 } } $$

Solution
Question 6
1 / -0

Two point charges $$q _ { 1 } \text { and } q _ { 2 }$$ terminates at are kept as shown.
One of the electric field line coming out from $$q _ { 1 }$$ makes an angle $$30 ^ { \circ }$$ with the line joining $$q _ { 1 } q _ { 2 }$$ terminates at $$q _ { 2 }$$ makes an angle $$60 ^ { \circ }$$.The ratio $$\frac { q _ { 1 } } { q _ { 2 } }$$ is

A
$$\frac { 1 } { 2 - \sqrt { 3 } }$$

B
$$-\frac { 1 } { 2 - \sqrt { 3 } }$$

C
$$\frac { - 1 } { 2 }$$

D
$$2$$

Solution
Question 7
1 / -0

A charge q is divided into two parts q $$\left(q-q\right)$$. If the coulomb repulsion between them when they are separated is to be maximum the ratio of $$q/q$$ should be:

A
$$1/4$$

B
$$4$$

C
$$1/2$$

D
$$2$$

Solution
Question 8
1 / -0

Two identical metal balls with charges $$+2Q$$ and $$-Q$$ are separated by some distance and exert a force $$F$$ on each other. They are joined by a conducting wire, which is then removed. The magnitude force between them will now be

A
$$F$$

B
$$\dfrac{F}{2}$$

C
$$\dfrac{F}{4}$$

D
$$\dfrac{F}{8}$$

Solution

Hint: As the balls are identical their capacitance would be same but potentials are different. Therefore transfer of charge took place after connecting them by wire until both balls gain equal amount of charge.
Solution:
Step-1: Calculate Coulomb force before connecting wire
Let $$\mathrm{r}$$ be the distance between charges and $$\mathrm{k}=$$ Coulomb constant Magnitude of Coulomb force between charge $$+2 Q$$ and $$-Q$$ is
$$\therefore \quad \mathrm{F}=\left|\frac{k \times(+2 Q) \times(-Q)}{r^{2}}\right|$$
$$\Rightarrow F=\frac{2 k Q^{2}}{r^{2}}$$
Step-2: Coulomb force after connecting the wire
After connecting the balls by wire both balls will have same charge
Hence charge of each ball $$=\frac{\text { net charge }}{\text { number of charge }}$$
$$=\frac{(+2 Q)+(-Q)}{2}$$
$$=\frac{Q}{2}$$
Now magnitude of Coulomb force between the charges,
$$F^{\prime}=\left|\frac{k \times \frac{Q}{2} \times \frac{Q}{2}}{r^{2}}\right|=\frac{k Q^{2}}{4 r^{2}}$$
$$\therefore \quad \frac{F^{\prime}}{F}=\frac{\frac{k Q^{2}}{4 r^{2}}}{\frac{2 k Q^{2}}{r^{2}}}=\frac{1}{8}$$
$$\Rightarrow \quad F^{\prime}=\frac{F}{8}$$
$$\therefore$$ Answer is option $$D$$
Question 9
1 / -0

Six charges +Q each are placed at the corners of a regular hexagon of side (a), the electric field at the centre of hexagon is -

A
Zero

B
$$\frac { 1 }{ 4\pi { \epsilon }_{ 0 } } .\frac { 6{ Q }^{ 2 } }{ { a }^{ 2 } } $$

C
$$\frac { 1 }{ 4\pi { \epsilon }_{ 0 } } .\frac { { Q }^{ 2 } }{ { a }^{ 2 } } $$

D
$$\frac { 1 }{ 4\pi { \epsilon }_{ 0 } } .\frac { 6{ Q }^{ 2 } }{ a\sqrt { 2 } } $$
Question 10
1 / -0

Two positive ions, each carrying a charge $$q$$ , are separated by a distance $$d$$. If $$F$$ is the force of repulsion between the ions, the number of electronsmissing from each ion will be (e being the charge on an electron)

A
$$\dfrac { 4 \pi \varepsilon _ { 0 } F d ^ { 2 } } { e ^ { 2 } }$$

B
$$\sqrt { \dfrac { 4 \pi \varepsilon _ { 0 } F e ^ { 2 } } { d ^ { 2 } } }$$

C
$$\sqrt { \dfrac { 4 \pi \varepsilon _ { 0 } F d ^ { 2 } } { e ^ { 2 } } }$$

D
$$\dfrac { 4 \pi \varepsilon _ { 0 } F d ^ { 2 } } { q ^ { 2 } }$$

Solution