Electric Potential Due to Shell

Q. Two charges + 2 μ C and + 8 μ C are placed at two vertices of equilateral triangle of side 1m. The potential at third vertex of the triangle isOptions:90 x 10v9 x 10 V0.9 x 10 V900 x 10 V

Q.

An electric dipole is at the centre of a hollow sphere of radius r, where Q is the charge and d is the distance between the two charges of the dipole. The total normal electric flux through the sphere

1. Q.d

2. 

3. 

4. zero

Q. Two conducting spheres of radii a and b respectively are charged and joined by a wire. The ratio of electric field due the spheres at their surfaces when isolated is

1. $\frac{b}{a}$
2. $\frac{a^2}{b^2}$
3. $\frac{a}{b}$
4. $\frac{b^2}{a^2}$

Q. What is de Broglie wavelength associated with an electron, accelerated through a potential difference of $64\text{V}$?

1. $0.451\text{nm}$
2. $0.361\text{nm}$
3. $0.153\text{nm}$
4. $0.281\text{nm}$

Q. An infinite, uniformly charged sheet with surface charge density (p) cuts through a spherical Gaussian surface of radius R at a distance x from its centre, as shown . The electric flux through the Gaussian surface is

Q. Two insulated charged conducting spheres of radii 20 cm and 15 cm respectively and having an equal charge of 10 C are connected by a copper wire and then they are separated. Then

1. Surface charge density on the 15 cm sphere will be greater than that on the 20 cm sphere
2. Both the spheres will have the same charge of 10 C
3. Surface charge density on the 20 cm sphere will be greater than that on the 15 cm sphere
4. Surface charge density on the two spheres will be equal

Q. A point charge $q$ is placed at a distance $r$ from the centre $O$ of a uncharged spherical conducting shell of inner radius $R$ and outer radius $2R$. The distance $r<R$. The electric potential at the centre of the shell will be

1. $\frac{q}{8\pi {ϵ}_{0}R}$
2. $\frac{q}{4\pi {ϵ}_{0}r}$
3. $\frac{q}{4\pi {ϵ}_0}[\frac{1}{r}-\frac{1}{2R}]$
4. $\frac{q}{4\pi {ϵ}_0}[\frac{1}{r}+\frac{1}{2R}]$

Q.

A $12.5eV$ electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?

Q. An electron (of mass $m$) and a photon have the same energy $E$ in the range of a few $\text{eV}$. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is ($c=$ speed of light in vacuum)

1. $\frac{1}{c}{\left(\frac{2E}{m}\right)}^{1/2}$
2. $c(2mE{)}^{1/2}$
3. $\frac{1}{c}{\left(\frac{E}{2m}\right)}^{1/2}$
4. ${\left(\frac{E}{2m}\right)}^{1/2}$

Q.

The electric flux of a surface is maximum, when

Q. 11.A spherical charge distribution is symmetrical about a point O.The volume charge density Rho depend upon the distance r from the point O as rho p(1-r/R).Find the total charge enclosed inside a sphere of Radius R having center at O

Q. A hollow conducting sphere of radius R has a charge (+Q) on its surface. What is the electric potential within the sphere at a distance $r=\frac{R}{3}$ from its centre

1. Zero
2. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{R}$
3. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{r}$
4. $\frac{1}{4\pi {ϵ}_0}\frac{Q}{r^2}$

Q. Two charged conducting spheres of radii r1 and r2 connect to each other by a wire . find the ratio of electric fields at the surface of the two spheres?

Q. Three concentric spherical metallic shells A, B and C of radii $a,b$ and $c(a<b<c)$ have surface charge densities $\sigma ,-\sigma$ and $\sigma ,$ respectively.
If $V_A,V_B$ and $V_C$ are potential of shells A, B and C, respectively, match the columns
$\begin{array}{cc}\text{Column A}& \text{Column B}\\ \text{a.}{V}_A& \text{i.}\frac{\sigma }{{\epsilon }_0}\left[\frac{a^2-b^2+c^2}{c}\right]\\ \text{b.}{V}_B& \text{ii.}\frac{\sigma }{{\epsilon }_0}[\frac{a^2}{b}-b+c]\\ \text{c.}{V}_C& \text{iii.}\frac{\sigma }{{\epsilon }_0}[a-b+c]\end{array}$

1. a − ii, b − iii, c − i
2. a − iii, b − ii, c − i
3. a − iii, b − i, c − ii
4. a − i, b − ii, c − iii

Q. four point charges -Q, -q, 2q and 2Q are placed one at each corner of the square. the relation between Q and q for which the potential at the centre of the squar is zero is:

Q. A hollow metal sphere of radius 5 cm is charged so that the potential on its surface is 10 V. The potential at the centre of the sphere is

1. Same as at point 25 cm away from the surface
2. Same as at point 5 cm away from the surface
3. 10 V
4. 0 V

Q.

What are electrostatic shielding and its applications?

Q. A circular wire loop of radius $r$ carries a total charge $Q$ distributed uniformly over its length. A small length $dl$ of the wire is cut off. The electric field at the centre due to the remaining wire is:-

1. $\frac{Qdl}{8{\pi }^2{ϵ}_0{r}^3}$
2. $\frac{Qdl}{2{\pi }^2{ϵ}_0{r}^3}$
3. $\frac{Qdl}{8\pi {ϵ}_0{r}^3}$
4. $\frac{Qdl}{4{\pi }^2{ϵ}_0{r}^3}$

Q. two metallic spheres of radii 1 cm and 2 cm are given charges 10^-2 and 5*10^-2 respectively. if they are connected by a conducting wire the final charge on smaller sphere is?

Q. A spherical conductor of radius 2m is charged to a potential of 120 V. It is now placed inside another hollow spherical conductor of radius 6m. Calculate the potential to which the bigger sphere would be raised to?

1. 20 V
2. 60 V
3. 40 V
4. 80 V

Q. Equal charges are given to two conducting spheres of different radii. The potential will be

1. more on the smaller sphere
2. more on the bigger sphere
3. equal on both the spheres
4. Dependent on the nature of the materials of the spheres

Q. A spherical conductor is placed near another positively charged conductor. The net charge acquired by spherical conductor will be(1) Either positive or negative(2) Positive only(3) Negative only(4 Zero

Q. 13.What is the electric field at centre of uniformly charged quarter circle

Q. A charge ‘q’ is placed at the centre of a conducting spherical shell of radius $R$, which is given a charge 'Q'. An external charge Q' is also present at distance $R^{\prime }(R^{\prime }>R)$ from ‘q’. Then the resultant electric field will be best represented for region $r$ > R by: (where $r$ is the distance of the point from q)

1. 
2. 
3. 
4. 

Q.

The de-Broglie wavelength associated with an electron and a proton was calculated by accelerating them through the same potential of $100V$. What should nearly be the ratio of their wavelengths? $(m_p=1.00727u;m_e=0.00055u)$.

1. $\left(1860\right)2:1$

2. $43:1$

3. $1860:1$

4. $41.4:1$

Q. 45.A small spherically symmetric charge q is placed at one vertex of a cube as shown in fig. The flux through the faves ABCD and HGEF are,

Q. Charges $+q$ and $-q$ are placed at the vertices $\text{B}$ and $\text{C}$ of an isosceles triangle. The potential at the vertex $\text{A}$ is

1. $\frac{1}{4\pi {ϵ}_0}.\frac{2q}{\sqrt{a^2+b^2}}$
2. zero
3. $\frac{1}{4\pi {ϵ}_0}.\frac{q}{\sqrt{a^2+b^2}}$
4. $\frac{1}{4\pi {ϵ}_0}.\frac{-q}{\sqrt{a^2+b^2}}$

Q. A charge $q=1\mu C$ is placed at point $(1\text{m},2\text{m},2\text{m})$. Find the magnitude of electric field at point $(0\text{m},1\text{m},1\text{m})$

1. $1\times {10}^3\text{N/C}$
2. $2\times {10}^3\text{N/C}$
3. $3\times {10}^3\text{N/C}$
4. $4\times {10}^3\text{N/C}$

Q. A point charge is placed at $A(3,4)\text{m}$ in $xy$ plane then electric field at origin is $E$. If charge is moved from $A$ to $B$ $(24,7)\text{m}$ then electric field at origin is:-

1. $\frac{E}{25}$
   
2. $25E$
3. $5E$
4. $\frac{E}{5}$
   

Q. An insulator solid sphere of radius R is charged in a uniform manner such that volume charge density p=A/r where A is constant, r is distance from the centre. Electric field strength at any inside point at a radial distance r is?