Gauss's Law

Q.

A point charge of 2.0 $\mu$C is at the centre of a cubic Gaussian
surface 9.0 cm on edge. What is the net electric flux through the
surface?

Q.

Electric charge is uniformly distributed along a long straight wire of radius 1 mm. The charge per cm length of the wire is Q coulomb . Another cylindrical surface of radius 50 cm and length 1 m symmetrically encloses the wire as shown in the figure. The total electric flux passing through the cylindrical surface is

1. 
2. 
3. 
4. 

Q.

A long cylindrical volume contains a uniformly distributed charge of density $\rho$. Find the electric field at a point P inside the cylindrical volume at a distance x from its axis (figure 30-E5)

Q. four particles each having charge q, are placed on the four vertices of a regular pentagon . the dis†an ce of each corner from the centre is a. find the electric field at th centre of pentagon

Q.

If the radius of the gaussian surface enclosing a charge is halved, how does the electric flux through the Gaussian surface change?

Q.

The dimension of $(1/2){\epsilon }_0{E}^2$${\epsilon }_0$ is the permittivity of free space, $E$ is the electric field

1. $\left[ML{T}^{-1}\right]$

2. $\left[M{L}^2{T}^{-2}\right]$

3. $\left[M{L}^{-1}{T}^{-2}\right]$

4. $\left[M{L}^2{T}^{-1}\right]$

Q.

What is the electric flux through a cube of side $1\mathrm{cm}$ which encloses an electric dipole?

Q.

Difference between plane angle and solid angle

Q. The total flux associated with given cube will be, where ${}^{\prime }{a}^{\prime }$ is side of cube :–
$(\frac{1}{{ϵ}_o}=4\pi \times 9\times {10}^9)$

1. $162\pi \times {10}^{-3}\frac{{\text{Nm}}^2}{\text{C}}$
   
2. $162\pi \times {10}^3\frac{{\text{Nm}}^2}{\text{C}}$
   
3. $162\pi \times {10}^{-6}\frac{{\text{Nm}}^2}{\text{C}}$
   
4. $162\pi \times {10}^6\frac{{\text{Nm}}^2}{\text{C}}$
   

Q. Careful measurement of the electric field at the surface of a blackbox indicates that the net outward flux through the surface of thebox is 8.0 × 103 Nm2/C. (a) What is the net charge inside the box? (b) If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Whyor Why not?

Q. Three charges each q are kept at 3 corners of a square as shown in fig and q /2 is at one corner . Electric field at the centre is

Q.
The electric flux for Gaussian surface A that enclose the charged particles in free space is $(given{q}_1=-14nC,q_2=78.85nC,q_3=-56nC)$

1. 10³ Nm² C^–1
2. 10³ CN^-1 m^–2
3. 6.32 X 10³ Nm² C^–1
4. 6.32 X 10³ CN^-1 m^–2

Q.

Which charge configuration produces a uniform electric field?

1. Point charge

2. Infinite uniform line charge

3. uniformly charged infinite plane

4. uniformly charged spherical shell

Q.

Gauss's law should be invalid if

1. The velocity of light were not a universal constant

2. There were magnetic monopoles

3. The inverse square law were not exactly true

4. None of these

Q.

Find the flux of the electric field through a spherical surface of radius R due to a charge of $10-7C$ at the centre and another equal charge at a point 2R away from the centre (figure 30-E2).the point P, the flux of the electric field through the closed surface

(a) will remain zero (b) will become positive

(c) will become negative (d) will become undefined .

Q. Figure shows the electric lines of force emerging from a charged body. If the electric field at A and B are $E_A$ and $E_B$ respectively and if the displacement between A and B is r then

1. $E_A>E_B$
2. $E_A<E_B$
3. $E_A=\frac{E_B}{r}$
4. $E_A=\frac{E_B}{r^2}$

Q.

A charge Q is placed at the centre of an imaginary hemispherical surface. Using symmetry arguments and the Gauss's law, find the flux of the electric field due to this charge through the surface of the hemisphere (figure 30-E3).

Q.

A charged shell of radius $R$carries a total charge $Q$. Given $\varphi$ as the flux of electric field through a closed cylindrical surface of height $h$, radius $r$ & with its center same as that of the shell. Here the center of the cylinder is a point on the axis of the cylinder which is equidistant from its top & bottom surfaces. Which of the following are correct.

1. $Ifh>2Randr>Rthen\varphi =Q/Єo$

2. $Ifh>2Randr=4R/5then\varphi =Q/5Єo$

3. $Ifh<8R/5andr=3R/5then\varphi =0$

4. $Ifh>2Randr=3R/5then\varphi =Q/5Єo$

Q. A cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux from the surface of the cylinder is

1. $2\pi R^{2}E$
2. $\pi R^2/E$
3. $(\pi R^2-\pi R)/E$
4. Zero

Q.

A charge Q is uniformly distributed over a rod of length l. Consider a hypothetical cube of edge l with the centre of the cube at one end of the rod.Find the minimum possible flux of the electric field through the entire surface of the cube.

Q. The inward and outward electric flux for a closed surface in units of $N-m^2/c$ are respectively $8\times {10}^3$ and $4\times {10}^3$. Then the total charge inside the surface is [where $ϵ$ = permittivity constant]

1. -4 X 10³ C
2. 
3. 
4. 4 X 10³ C

Q. The volume charge density as a function of distance $x$ from one face inside a unit cube is varying as shown in the figure. Then the total flux (in S.I. units) through the cube if $({\rho }_o=8.85\times {10}^{–12}\frac{C}{m^3})$ is :

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

Q.

Figure 20.17 shows a spherical Gaussian surface and a charge distribution. When calculating the flux of electric field through the Gaussian surface, the electric field will be due to

1. $+q_{1}and+q_3$

2. $+q_1,+q_{3}and-q_2$

3. $+q_{3}alone$

4. $+q_1,and-q_2$

Q. A point charge +$q$ is placed on the axis of a closed cylinder of radius $R$ and height $\frac{25R}{12}$ as shown. If electric flux coming out form the curved surface of cylinder is $\frac{xq}{10{\in }_0}$, then calculate $x$.

Q. The electric field in a region is radially outwards with magnitude $E=\alpha R$. Calculate the charge contained in a sphere of radius $R$ centred at the origin. If the value of charge is $m\times {10}^{-10}C$, then find $m$. (Given $\alpha =100V/m^2$ and $R=0.30m$)

Q.

A parallel plate capacitor whose capacitance $C$ is $14pF$ is charged by a battery to a potential difference $V=12V$ between its plates. The charging battery is now disconnected and a porcelain plate with $k=7$ is inserted between the plates, then the plate would oscillate back and forth between the plates, with a constant mechanical energy of $\_\_\_\_pJ.$. (Assume no friction)

Q. Choose the graph that represents the variation of potential $\left(V\right)$ versus distance from the centre of ring along its axis $\left(r\right)$ for a uniform ring of change $Q$.

1. 
2. 
3. 
4. 

Q.

Write some important characteristics of electric field lines.

Q. A point charge causes an electric flux of –1.0 × 103 Nm2/C to pass through a spherical Gaussian surface of 10.0 cm radius centred onthe charge. (a) If the radius of the Gaussian surface were doubled, how much flux would pass through the surface? (b) What is thevalue of the point charge?

Q.

What is null point