Introducing Flux

Q. Two pith balls carrying equal charges are suspendedfrom a common point by strings of equal length, theequilibrium separation between them is r. Now thestrings are rigidly clamped at half the height. Theequilibrium separation between the balls now become0孁ㄧ寵尊@㈱諧竊㈱“1驉套1糊爺章載莓■u宿■顱員y/2

Q.

Two identical conducting spheres with negligible volume have $2.1nC$ and $-0.1nC$ charges, respectively. They are brought into contact and then separated by a distance of $0.5m$. The electrostatic force acting between the spheres is _______$\times {10}^{-9}N$. [Given : $4{\mathrm{\pi \epsilon }}_0=\frac{1}{9}\times {10}^{-9}$ SI unit]

Q. A deuteron and an α -particle are placed in an electric field. The force acting on them are F1 and F2 and theiraccelerations are a, and a2 respectively, then(2) F, > F2(4) a1 #a22

Q.

Consider a uniform electric field $E=3\times {10}^3\hat{i}N/C$.
(a) What is the flux of this field through a square of 10 cm on a side whose plane is parallel to the yz plane?
(b) What is the flux through the same square if the normal to its plane makes a 60° angle with the x-axis?

Q. An electric field is uniform, and in the positive x direction for positive x, and uniform with theame magnitude but in the negative x direction for negative x. It is given that Е-200i(NC)forx > 0 and Ε -200i(NC) for x < 0. A right circular cylinder of length 20 cm and radius(a) What is the net outward flux through each flat face?(c) What is the net outward flux through the cylinder?5 cm has its centre at the origin and its axis along the x-axis so that one face is at x +10cm and the other is at x-10 cm(b) What is the flux through the side of the cylinder?2.(d) What is the net charge inside the cylinder?

Q.

What is the net flux of the uniform electric field through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?

Q. the linear charge density upon the semi circular ring on both side is same in magnitude the electric field at O is alon

Q. Two charges of magnitudes - 2Q and +Q are located at points (a, 0) and (4a, 0) respectively. What is the electric flux due to these charges through a sphere of radius '3a' with its centre at the origin ?

Q. 40. There is uniform electric field of 8 i N/C. What is the net flux of the uniform electric field through the cube of side 0.3m oriented so that its faces are parallel to the coordinate plane

Q. Given a uniform electric field E = 5 x 10° i^ N/C. Find the flux of this field through a square of side 10 cm on a side whose plane is parallel to the y-z plane. What would be the flux through the same square if the plane makes a 30° angle with the X-axis ?

Q. A uniformly charged disc of radius $R$ having surface charge density $\sigma$ is placed in the $XY$ plane with its center at the origin. Find the electric field intensity along the $z$-axis at a distance $Z$ from origin.

1. $E=\frac{\sigma }{2{\epsilon }_0}(1-\frac{Z}{(Z^2+R^2{)}^{1/2}})$
2. $E=\frac{\sigma }{2{\epsilon }_0}(\frac{1}{(Z^2+R^2)}+\frac{1}{Z^2})$
3. $E=\frac{2{\epsilon }_0}{\sigma }(\frac{1}{(Z^2+R^2{)}^{1/2}}+Z)$
4. $E=\frac{\sigma }{2{\epsilon }_0}(1+\frac{Z}{(Z^2+R^2{)}^{1/2}})$

Q. A point charge +q is placed on the axis of a ring of radius R at distance r from the centre , then electric flux through the ring due to the point charge will be

Q.

Two isolated conducting spheres $S_1$ and $S_2$ of radius $\left(\frac{2}{3}\right)R$ and $\left(\frac{1}{3}\right)R$ have $12\mu C$ and $-3\mu C$ charges, respectively, and are at a large distance from each other. They are now connected by a conducting wire. A long time after this is done the charges on $S_1$ and $S_2$ are respectively.

1. $6\mu Cand3\mu C$

2. $4.5\mu Conboth$

3. $+4.5\mu Cand-4.5\mu C$

4. $3\mu Cand6\mu C$

Q. A certain charge $Q$ is divided at first into two parts, $\left(q\right)$ and $(Q-q)$. Later on the chrages are placed at a certain distance. If the force of interaction between the two charges is maximum, then

1. $\left(Q/q\right)=\left(4/1\right)$
2. $\left(Q/q\right)=\left(2/1\right)$
3. $\left(Q/q\right)=\left(3/1\right)$
4. $\left(Q/q\right)=\left(5/1\right)$

Q.

The electric field in a region is given by $\overrightarrow{E}=\frac{3}{5}{E}_0\overrightarrow{j}$ with $E_0=2.0\times {10}^{3}N{C}^{-}1$. Find the flux of this field through a rectangular surface of area $0.2m^2$ parallel to the y-z plane.

Q.

In an NPN transistor the collector current is $24mA$. If $80\%$ of electrons reach collector its base current in $mA$ is?

Q.

A large plane charge sheet having surface charge density $\sigma =2.0\times {10}^{-6}C{m}^{-2}$ lies in the x-y plane. Find the flux of the electric field through a circular area of radius $1cm$ lying completely in the region where x, y, z are all positive and with its normal making an angle of ${60}^{\circ }$ with the z-axis. (Given that the field due to infinite charged sheet is $\frac{\sigma }{2{ϵ}_0}$ where $\sigma$ = surface charge density. Also note that it is perpendicular to the sheet and is constant for all points from the sheet.)

1. $35\frac{N{m}^2}{C}$

2. $35\frac{C}{N{m}^2}$

3. $17.5\frac{N{m}^2}{C}$

4. $17.5\frac{C}{N{m}^2}$

Q. In a coil of resistance $10\Omega$, the induced current developed by changing magnetic flux through it, as shown in figure is a function of time. The magnitude of change in flux through the coil in $\text{weber}$ is:

1. $8$
2. $2$
3. $6$
4. $4$

Q.

Two non-conducting spheres of radii R_1​ and R₂​ and carrying uniform volume charge densities +ρ and −ρ, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,

1. The electrostatic field is zero

2. The electrostatic potential is constant

3. The electrostatic field is constant in magnitude

4. The electrostatic field has the same direction

Q.

Electric flux: scalar or a vector quantity?

Q. A uniform electric field $E=500N/C$ passes through a hemispherical surface of radius $R=1.2m$ as shown in the figure. The net electric flux (in SI units) through the hemispherical surface only in $N\pi$. Find the value of N.

Q. A point charge q is placed at a distance l from the centre of a disc of radius R along its axis. The electric flux through the disc is

1. 
   

2. 
   

3. 
   

4. 
   

Q. A point charge $q_1=-5.8\mu \text{C}$ is held stationary at the origin. A second charge $q_2=+4.3\mu \text{C}$ moves from the point $(0.26\text{m},0,0)$ to $(0.38\text{m},0,0)$. Find the workdone by the electric force on $q_2$.

1. $-0.272\text{J}$
2. $+0.272\text{J}$
3. $-0.381\text{J}$
4. $+0.381\text{J}$

Q. A long solid non-conducting cylinder of radius $10\text{cm}$ contains a uniformly distributed charge of density $10{\text{nC/m}}^3$. Find the magnitude of electric field at a point $\text{P}$ inside the cylindrical volume at a distance $5\text{cm}$ from its axis.
(Take ${ϵ}_o=9\times {10}^{-12}{\text{C}}^2/{\text{N-m}}^2$)

1. $17.8\text{N/C}$
2. $27.8\text{N/C}$
3. $37.8\text{N/C}$
4. $47.8\text{N/C}$

Q.

Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon?

Q. Consider a uniform spherical charge distribution of radius $R_1$ centred at the origin O. In this distribution, a spherical cavity of radius $R_2$, centre at P with distance $OP=\alpha =R_1-R_2$ is made. If the electric field inside the cavity at position $\overrightarrow{r}$ is $\overrightarrow{E}\left(\overrightarrow{r}\right)$, then the correct statement(s) is (are)

1. $\overrightarrow{E}$ is uniform, its magnitude is independent of $R_2$ but its direction depends on $\overrightarrow{r}$
2. $\overrightarrow{E}$ is uniform, its magnitude is depends on $R_2$ and its direction depends on $\overrightarrow{r}$
3. $\overrightarrow{E}$ is uniform, its magnitude is independent of $\alpha$ but its direction depends on $\overrightarrow{\alpha }$
4. $\overrightarrow{E}$ is uniform and both its magnitude and direction depend on $\overrightarrow{\alpha }$

Q. Two points charges $Q_1$ and $Q_2$ are placed at separation $d$ in vacuum and force acting between them is $F$. Now a dielectric slab of thickness $\frac{d}{2}$ and dielectric constant $K=4$ is placed between them. The new force between the charges will be

1. $\frac{4F}{9}$
2. $\frac{2F}{9}$
3. $\frac{F}{9}$
4. $\frac{5F}{9}$

Q.

A uniformly charged conducting sphere of 2.4 m diameter has a
surface charge density of 80.0 $\mu C/m^2$.
Find the charge on the sphere.

What is the total electric flux leaving the surface of the
sphere?

Q. In the x-y-plane, the region $y>0$ has a uniform magnetic field $B_1\hat{k}$ and the region $y<0$ has another uniform magnetic field $B_2\hat{k}$. A positively charged particle is projected from the origin along the positive $y$-axis with speed $V_o=\pi m{s}^{-1}$ at $t=0$, as shown in the figure. Neglect gravity in this problem. Let $t=T$ be the time when the particle crosses the x-axis from below for the first time. If $B_2=4B_1$, the average speed of the particle, in $m{s}^{-1}$, along the x-axis in the time interval $T$ is

Q. A charge $Q$ is divided into two parts $q$ and $Q-q$. Find the relationship between $Q$ and $q$ , if the two parts placed at a given distance $r$ apart have the maximum coulomb repulsion force?

1. $q=\frac{Q}{2}$
2. $q=\frac{Q}{3}$
3. $q=\frac{2Q}{2}$
4. $q=\frac{Q}{4}$