Charging by Induction

Q. Two equal negative charge – q are fixed at the fixed points (0, a) and (0, -a) on the Y-axis. A positive charge Q is released from rest at the point on the X-axis. The charge Q will

1. Execute simple harmonic motion about the origin
2. Move to the origin and remain at rest
3. Move to infinity
4. Execute oscillatory but not simple harmonic motion

Q. An object has charge of $1\text{C}$ and gains $5.0\times {10}^{18}$ electrons. The net charge on the object becomes –

Q.

What will happen to the leaves of electroscope if positively charged body is brought near (a) uncharged electroscope (b) positively charged electroscope (c) negatively charged electroscope ?

Q.

Two points charges $4q$ and$–q$ are fixed on the$x-$axis at $x=\frac{-d}{2}$ and $x=\frac{d}{2}$, respectively. If a third point charge $‘q’$is taken from the origin to $x=d$ along the semicircle as shown in the figure, the energy of the charge will:

1. decrease by $\frac{q^2}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}\mathrm{d}}$

2. decrease by $\frac{4q^2}{3{\mathrm{\pi \epsilon }}_{\mathrm{o}}\mathrm{d}}$

3. increases by$\frac{3q^2}{4{\mathrm{\pi \epsilon }}_{\mathrm{o}}\mathrm{d}}$

4. decrease by $\frac{2q^2}{3\mathrm{\pi }{\epsilon }_{\mathrm{o}}\mathrm{d}}$

Q.

The electric potential at a point in free space due to charge $Q$ coulomb is $Q\times {10}^{11}V$. The electric field at that point is

1. $12\pi {\epsilon }_{0}Q\times {10}^{22}V/m$

2. $4\pi {\epsilon }_{0}Q\times {10}^{22}V/m$

3. $12\pi {\epsilon }_{0}Q\times {10}^{20}V/m$

4. $4\pi {\epsilon }_{0}Q\times {10}^{20}V/m$

Q. A point charge $q$ is placed at the origin. Let ${\overrightarrow{E}}_A,{\overrightarrow{E}}_B$ and ${\overrightarrow{E}}_C$ be the electric fields at three points, $A(1,2,3)$, $B(1,1,–1)$ and $C(2,2,2)$ due to charge $q$. Then

$\left(i\right){\overrightarrow{E}}_A\perp {\overrightarrow{E}}_B$
$\left(ii\right)\left|\begin{array}{c}{\overrightarrow{E}}_B\end{array}\right|=4\left|\begin{array}{c}{\overrightarrow{E}}_C\end{array}\right|$

Select the correct alternative.

1. Only $\left(i\right)$ is correct.
2. Only $\left(ii\right)$ is correct.
3. Both $\left(i\right)$ and $\left(ii\right)$ are correct.
4. Both $\left(i\right)$ and $\left(ii\right)$ are wrong.

Q.

An infinite number of charges, each equal to 4C, are placed along the x-axis at x = 1 m, x = 2 m, x = 4 m, x = 8 m and so on. The total force on a charge of 1C placed at the origin is

1. 48 × 10 ⁴ N

2. 48 × 10 ⁸ N

3. 4.8 × 10 ⁹ N

4. 4.8 × 10 ¹⁰ N

Q. A capacitor of capacitance $C$ is charged by connecting it to a battery of emf $E$. The capacitor is now disconnected and reconnected to the battery with the polarity reversed. The heat developed in the connecting wires is:

1. $2C{E}^2$
2. $C{E}^2$
3. $\frac{C{E}^2}{4}$
4. $\frac{3}{2}C{E}^2$

Q. Consider the charge configuration and spherical Gaussian surface as shown in the figure. When calculating the flux of the electric field over the spherical surface the electric field will be due to

1. $q_2$
2. Only the positive charges
3. All the charges
4. $+q_1$ and $-q_1$

Q. Four electric charges +q, +q, -q and-q are placed at the corners of a square of side 2L .The electric potential at point A, midway between the two charges + and +q, is

Q. two plates (area =s) charged to +q1 and +q2 (q2>q1) are brought close to form capacitor of capacitance C. the potential difference across the plates is -

Q. A metallic solid sphere is placed in a uniform electric field. The electric lines of force follow the path(s) shown in the figure as

1. $1$
2. $2$
3. $3$
4. $4$

Q.

What is the SI unit of electric flux?

Q. When a body is charged by induction, then the body

1. becomes neutral
2. does not lose any charge
3. loses whole of the charge on it
4. loses part of the charge on it

Q. If a charged body is placed near a neutral conductor, then

1. It will repel the conductor
2. It will attract the conductor
3. It will not exert either attractive or repulsive force on conductor
4. It may repel or attract conductor, depending on its shape

Q.

A charge of 5C experiences a force of 5000N when it is moved in a uniform electric field. The potential difference between two points separated by a distance of 1cm is?

Q.

(a) A conductor A with a cavity as shown in Fig. 1.36(a) is given a charge Q. Show that the entire charge must appear on the outer surface of the conductor. (b) Another conductor B with charge q is inserted into the cavity keeping B insulated from A. Show that the total charge on the outside surface of A is Q + q [Fig. 1.36(b)]. (c) A sensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest a possible way.

Q. Two point charges $(Q$ each$)$ are placed at $(0,y)$ and $(0,–y)$. A point charge $q$ of the same polarity can move along $x-$axis. Then:

1. The force on $q$ is maximum at $x=\pm \frac{y}{\sqrt{2}}$.
2. The charge $q$ is in equilibrium at the origin.
   
3. The charge $q$ performs an oscillatory motion about the origin.
   
4. For any position of $q$ other than origin, the force is directed away from the origin.
   

Q.

The tire of aircraft is made of special rubber which makes them slightly conducting, Explain the reasons for using special rubber.

Q.

Two identical metal spheres P and Q are supported on insulating stands and placed in contact. What kind of charges will P and Q develop when a negatively charged ebonite rod is brought near P?

1. P will have a positive charge and Q will have a negative charge

2. P will have a negative charge and Q will have a positive charge

3. Both p and Q will have positive charge

4. Both p and Q will have negative charge

Q.

A hollow metal sphere of radius $10cm$ is charged such that the potential on its surface is $80volt.$ The potential at the center of the sphere is

Q. The effective capacitance between $\text{A}$ and $\text{B}$ is

1. $\frac{C}{4}$
2. $\frac{3C}{4}$
3. $\frac{C}{3}$
4. $\frac{4C}{3}$

Q.

What Is Conventional Current?

Q. Two conductors of the same shape and size. one of Copper and the other of aluminium ( less conducting) are placed in an uniform electric field. The charge induced in aluminium A) will be less than in copper B) will be more than in copper C) will be equal to that of copper

Q.

Force of attraction between two point electric charges placed at a distance"d" in a medium is "F". What distance apart should these be kept in the same medium, so that force between them become F/3?

Q. A glass slab (K=10) is introduced between two parallel plates and then the plates are charged.The surface charge density of charge on the plates is 10^{-6}C/m^2 .The surface charge denssity of polarised charge is ?

Q.

How can we say that charge acquired by glass rod is positive while for ebonite rod it is negative?

Q.

A particle of charge $q$ and mass $m$ is moving with velocity $-v\hat{i}$ $\left(v\ne 0\right)$ towards a large screen placed in the $Y-Z$ plane at a distance $d$. If there is a magnetic field $B=B_0\hat{k}$, the minimum value of $v$ for which the particle will not hit the screen is:

1. $\frac{qd{B}_0}{m}$

2. $\frac{qd{B}_0}{3m}$

3. $\frac{2qd{B}_0}{m}$

4. $\frac{qd{B}_0}{2m}$

Q. Two identical conductors of copper and aluminium are placed in an identical electric fields. The magnitude of induced charge in the aluminium will be

1. Greater than in copper
2. Equal to that in copper
3. Zero
4. Less than in copper

Q.

A photocopier is a machine that makes paper copies of documents and other visual images quickly and cheaply. Most current photocopiers use a technology in which toner particles are positively charged and then transfer them onto paper in the form of an image/letters.

What charge should the paper possess for this process to happen?

1. Only Negative

2. Only Positive

3. Only Neutral

4. both b and c