Tag: static electricity

Questions Related to static electricity

The linear charge density of a thin metallic rod varies with the distance $'x'$ from one end as $\lambda  = {\lambda _0}{x^2}\left( {0 \leqslant x \leqslant l} \right).$ The total charge on the rod is:

physics static electricity exchange of electrons methods used for charging electric charge

  1. $\dfrac{{{\lambda _0}{l^3}}}{3}$

  2. $\dfrac{{{\lambda _0}{l^4}}}{3}$

  3. $\dfrac{{2{\lambda _0}{l^3}}}{3}$

  4. $\dfrac{{{\lambda _0}{l}}}{2}$

Show answer
Correct Option: D
Explanation:
$\lambda =\dfrac {\lambda _0 x}{L}$
$Q=\displaystyle \int _0^L \lambda \ dx$
$=\displaystyle \int _0^L \dfrac {\lambda _0 x}{L}dx$
$=\dfrac {\lambda _0}{L} \dfrac {x^2}{2}\displaystyle \int _0^L$
$=\dfrac {\lambda _0}{L}\times \dfrac {L^2}{2}$
$=\dfrac {\lambda _0L}{2}$

A hollow metal sphere, Sphere A, sits on an insulating stand. Sphere A has a diameter of 4 inches, and a net charge of magnitude $Q _0$. A second hollow metal sphere, Sphere B, also sits on an insulating stand, but has a diameter of 8 inches and zero net charge. The two spheres are brought close so that they touch, then they are separated.
In terms of $Q _0$, what is the final charge on Sphere A?

physics static electricity exchange of electrons methods used for charging electric charge

  1. $\cfrac{Q _0}{5}$

  2. $\cfrac{Q _0}{4}$

  3. $\cfrac{Q _0}{2}$

  4. $Q _0$

  5. $4Q _0$

Show answer
Correct Option: A
Explanation:

$R _B=2R _A$


Let final charge on spheres be $Q _A$ and $Q _B$.

On touching the spheres charge density becomes same.

And, charge density, $\sigma=\dfrac{Q}{4\pi R^2}$

$\implies Q\propto R^2$ for same $\sigma$

Hence, $\dfrac{Q _B}{Q _A}=\dfrac{R _B^2}{R _A^2}=2^2$

$\implies Q _B=4Q _A$

And, total charge$=Q _B+Q _A=Q _o$

$\implies 4Q _A+Q _A=Q _o$

$\implies Q _A=\dfrac{Q _o}{5}$

Answer-(A)

The number of electrons that must be removed from an electrically neutral silver dollar to give it a charge of $+2.4C$ is

physics static electricity explaining static electricity charging by induction electric charges and fields

  1. $2.5\times { 10 }^{ 19 }$

  2. $1.5\times { 10 }^{ 19 }$

  3. $1.5\times { 10 }^{ -19 }$

  4. $2.5\times { 10 }^{ -19 }$

Show answer
Correct Option: B
Explanation:

Total charge, $q=+2.4C$
Then by quantization of charge $q=ne$
$\therefore$ number of electrons, $\quad n=\cfrac { q }{ e } =\cfrac { 2.4C }{ 1.6\times { 10 }^{ -19 } } =1.5\times { 10 }^{ 19 }\quad \quad $

Induction is possible

physics electric charges and fields explaining static electricity charging by induction static electricity

  1. Only in conductor

  2. Only in insulator

  3. Both in conductor and insulator

  4. None of these

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Correct Option: C

When a glass rod is rubbed with silk it gains positive charge,because 

physics electric charges and fields explaining static electricity charging by induction static electricity

  1. Electrons are removed from it

  2. Protons are removed from it

  3. Proton are added to it

  4. Electron are added to it

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Correct Option: A

The process due to which an uncharged body acquires electric charges when held near a charged body is called :

physics electric charges and fields explaining static electricity charging by induction static electricity

  1. conduction

  2. induction

  3. convection

  4. none of these

Show answer
Correct Option: B
Explanation:

Answer is B.

If a negatively charged object is used to charge a neutral object by induction, then the neutral object will acquire a positive charge. And if a positively charged object is used to charge a neutral object by induction, then the neutral object will acquire a negative charge.
Hence, the process due to which an uncharged body acquires electric charges when held near a charged body is called induction.

When a glass rod is rubbed with silk, the charge acquired by the silk is :

physics electric charges and fields explaining static electricity charging by induction static electricity

  1. negative

  2. positive

  3. partly positive and partly negative

  4. none of these

Show answer
Correct Option: A
Explanation:

When a glass rod is rubbed with silk and brought near a GLE, the leaves of the GLE appear to diverge further.
When the glass rod touches the brass of the disc of the GLE, the free electrons from it flow to the glass rod. This causes a deficiency of electrons on the brass disc. To make up for this deficiency the electrons from the fold leaves flow towards the disc. This in turn causes electron deficiency on the gold leaves. As gold leaves as positively charged, they repel each other and hence diverge. Therefore the glass rod has a negative charge.
Hence, the charge acquired by the silk is negative charge.

A glass rod rubbed with silk is brought near the fur rubbed with an ebonite rod. What will be your observation between them?

physics electric charges and fields explaining static electricity charging by induction static electricity

  1. Attraction

  2. Repulsion

  3. No change

  4. cant say

Show answer
Correct Option: B
Explanation:

Rubbing the glass rod with the silk makes it lose electrons, so it becomes positively charged.similarly rubbing the fur with the ebonite makes it lose electrons and becomes positively charged.
Since, both glass rod and fur are positively charged and like charges repel each other. So, both the glass rod and fur will repel each other.

Charging by friction is accompanied by loss or gain of electrons. State which body loses electrons when an ebonite rod is rubbed with fur.

physics electric charges and fields explaining static electricity charging by induction static electricity

  1. $ebonite$

  2. $fur$

  3. $hand$

  4. $Both\ fur\ and\ ebonite$

Show answer
Correct Option: B
Explanation:

On rubbing an ebonite rod with fur or cat's skin, the electrons from the fur gets transferred to the ebonite rod. The fur now has a deficiency of electrons and so is positively-charged. On the other hand, the ebonite rod has an excess of electrons and hence is negatively-charged. In the above example, the fur undergoes positive electrification. It should be noted that it is the electrons and not the protons that get transferred during positive (and negative) electrification.
Therefore, in this case of electric conduction, the fur losses it electrons to the ebonite rod.

Charging by friction is accompanied by loss or gain of electrons. State which body loses electrons when a glass rod is rubbed with silk.

physics electric charges and fields explaining static electricity charging by induction static electricity

  1. $glass\ rod$

  2. $silk$

  3. $hand$

  4. $both\ glass\ rod\ and\ silk$

Show answer
Correct Option: A
Explanation:

On rubbing a glass rod with silk, the electrons from the glass rod get transferred to the silk. The silk now has an excess of electrons and so is negatively-charged. On the other hand, the glass rod is deficient in electrons and hence is positively-charged.
In the above example, the silk undergoes negative electrification.
Therefore, in this case of conduction, the glass rod losses it electrons to the silk.