Gauss's Law

Q. The spheres shown in the figure are connected by a conductor. The capacitance of this setup will be

1. $4\pi {ϵ}_0\frac{b^2}{(b-a)}$
2. $4\pi {ϵ}_{0}b$
3. $4\pi {ϵ}_0\frac{ab}{(b-a)}$
4. $4\pi {ϵ}_{0}a$

Q. The spheres shown in the figure are connected by a conductor. The capacitance of this setup will be

1. $4\pi {ϵ}_{0}b$
2. $4\pi {ϵ}_0\frac{ab}{(b-a)}$
3. $4\pi {ϵ}_{0}a$
4. $4\pi {ϵ}_0\frac{b^2}{(b-a)}$

Q. What are solid angles?

Q. A solid sphere with uniform charge distribution, of self energy $U_0$ and radius $R$ is divided into $n$ number of smaller spheres of radius $r$. The self energy of each smaller sphere is

1. $\frac{U_0}{n^{7/6}}$
2. $\frac{U_O}{n^{5/3}}$
3. $U=U_0{n}^{5/6}$
4. $\frac{U_O}{n^{5/6}}$

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. ${10}^{3}N{m}^2{c}^{-1}$
2. ${10}^{3}C{N}^{-1}{m}^{-2}$
3. $6.32\times {10}^{3}N{m}^2{C}^{-1}$
4. $6.32\times {10}^{3}C{N}^{-1}{m}^{-2}$

Q.

[MP PMT 1994, 95; DCE 1999, 2001; AIIMS 2001]

1. 

2. 

3. 

4. 

Q.

The figure shows an imaginary cube of length L/2 and a uniformly charged rod of length L touching the centre of the right face of the cube normally. At time t=0, the rod starts moving to the left slowly at a constant speed 'v'. the electric flux(F) through the cube is plotted against time(t). the correct graph showing the variation of flux with time is

1. 
2. 
3. 
4. 

Q. Find the flux through the circular disc due the point charge q.

1. $\frac{Q}{3{\epsilon }_0}cos\alpha$
2. $\frac{q}{2{\epsilon }_0}sin\alpha$
3. $\frac{q}{2{\epsilon }_0}(1-cos\alpha )$
4. $\frac{q}{2{\epsilon }_0}(1-sin\alpha )$

Q. Eight dipoles of charges of magnitude e are placed inside a cube. The total electric flux coming out of the cube will be

1. $\frac{8e}{{ϵ}_0}$
2. $\frac{16e}{{ϵ}_0}$
3. $\frac{e}{{ϵ}_0}$
4. $zero$

Q. Find the flux through the circular disc due the point charge q.

1. $\frac{Q}{3{\epsilon }_0}cos\alpha$
2. $\frac{q}{2{\epsilon }_0}sin\alpha$
3. $\frac{q}{2{\epsilon }_0}(1-cos\alpha )$
4. $\frac{q}{2{\epsilon }_0}(1-sin\alpha )$

Q. A point charge Q is placed just outside a cube of side 'a' near corner H. Flux of electric field associated with face ABCD is

1. $0$
2. $\frac{Q}{4{\epsilon }_0}$
3. $\frac{Q}{24{\epsilon }_0}$
4. $\frac{Q}{8{\epsilon }_0}$

Q. A charge is placed at the centre of an imaginary sphere. The flux through the sphere changes when its radius is changed.

1. False
2. True

Q.

The electric flux through the surface S as due to all the charges as shown in following figure is$\frac{q_1+q_3-q_2-q_4}{{ϵ}_0}$

1. True

2. false

Q. A uniformly charged ring is partially inserted into a hypothetical spherical surface as shown. Find the flux through the sphere. They are both of the same radius as shown and both pass through each other's centres.

1. $\frac{Q}{3{\epsilon }_0}$
2. $\frac{Q}{4{\epsilon }_0}$
3. $\frac{Q}{5{\epsilon }_0}$
4. $\frac{Q}{6{\epsilon }_0}$

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. $4\times {10}^{3}C$
2. $-4\times {10}^{3}C$
3. $\frac{(4\times {10}^3)}{ϵ}C$
4. $-4\times {10}^3{ϵ}_{0}C$

Q.

An electric dipole is an arrangement of two equal charges of equal magnitude but opposite nature, separated by some fixed distance.

Now consider a dipole enclosed inside a closed surface S. The flux through the surface S is zero.

1. True

2. false

Q.

Gauss law for magnetic field fetches a flux identically equal to zero because

1. Magnetic field obeys the superposition principle

2. Magnetic field changes with changing electric field

3. Magnetic monopoles can't exist theoretically

4. Magnetic monopoles have not been seen to exist

Q. Figure shows an imaginary cube of side $a$. A uniformly charged rod of length $a$ moves towards right at a constant speed $v$. At $t=0$, the right end of the rod just touches the left face of the cube. Which of the following represents the correct graph between electric flux passing through the cube with time?

1. 
2. 
3. 
4. 

Q.

Comment on the correctness of the following two statements:

Statement I => Gauss’s law is valid only for symmetrical Gaussian surfaces with respect to the charge distribution.

Statement II => Gauss’s law is valid only for charges placed in vacuum.

1. True, True

2. True, false

3. False, True

4. False, False

Q. $q_1,q_2,q_{3}and{q}_4$ are point charges located at points as shown in the figure and S is spherical Gaussian surface of radius R. Which of the following is true according to the Gauss’s law.

1. $\oint ({\overrightarrow{E}}_1+{\overrightarrow{E}}_2+{\overrightarrow{E}}_3).d\overrightarrow{A}=\frac{q_1+q_2+q_3}{2{ϵ}_0}$
2. $\oint ({\overrightarrow{E}}_1+{\overrightarrow{E}}_2+{\overrightarrow{E}}_3).d\overrightarrow{A}=\frac{q_1+q_2+q_3}{{ϵ}_0}$
3. $\oint ({\overrightarrow{E}}_1+{\overrightarrow{E}}_2+{\overrightarrow{E}}_3).d\overrightarrow{A}=\frac{q_1+q_2+q_3+q_4}{{ϵ}_0}$
4. $Noneoftheabove$

Q. Mark the incorrect statement(s), (Assume reference point to be at infinity)

1. Electric potential at the centre of a uniformly charged spherical shell due to its own charge is zero.
2. Electric potential at the centre of a uniformly charged sphere due to its own charge is zero.
3. Self energy of a dipole is positive.
4. If we change the reference point, the potential difference between 2 points will not change.

Q.

A charge q is located above the centre of a square plate of side a, at a distance $\frac{a}{2}$. The flux of electric field through the plate Is?

1. $\frac{q}{{ϵ}_0}$

2. $\frac{q}{2{ϵ}_0}$

3. $\frac{q}{4{ϵ}_0}$

4. $\frac{q}{6{ϵ}_0}$

Q. Electric field in the space is given as $\overrightarrow{E}=2x\hat{i}+y\hat{j}$, then charge enclosed inside cube of side length $2m$ as shown in figure will be

1. $12{ϵ}_0$
2. $24{ϵ}_0$
3. $-6{ϵ}_0$
4. $8{ϵ}_0$

Q.

A spherical volume contains a uniformly distributed charge of volume density $2.0\times {10}^{-4}C{m}^{-3}$. Find the strength of electric field at a point inside the volume at a distance $4.0cm$ from the centre.

1. $3\times {10}^4\frac{N}{C}$

2. $3\times {10}^5\frac{N}{C}$

3. $3\times {10}^6\frac{N}{C}$

4. $3\times {10}^7\frac{N}{C}$

Q.

Comment on the correctness of the following two statements based on the given situation.
Consider a line of length ‘l’ and uniform charge density $\lambda$. Assume a Gaussian surface S, a cylinder of radius R and height h.

Statement 1: $\phi =fluxthroughS=\frac{\lambda H}{{ϵ}_0}$

Statement 2: $|\overrightarrow{E}|atallthepointsonitscurvedsurface=\frac{\lambda }{{ϵ}_{0}2\pi R}$

1. True, True

2. True, false

3. False, True

4. False, False

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

1. $\frac{Q}{{ϵ}_0}$
2. $\frac{100Q}{{ϵ}_0}$
3. $\frac{10Q}{\left(\pi {ϵ}_0\right)}$
4. $\frac{100Q}{\left(\pi {ϵ}_0\right)}$

Q.

Electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius $10\text{cm}$ containing the total charge is $25\text{V-m}$. The flux through a concentric sphere of radius $20\text{cm}$ will be?

1. 25 V-m

2. 50 V-m

3. 100 V-m

4. 200 V-m