Tag: physics

Questions Related to physics

The electrostatic potential $V$ at any point (x, y, z) in space is given by $V = 4x^2$

  1. The y-and z-components of the electrostatic field at any point are zero.

  2. The x-component of electric field an any point is given by $(-8x \hat{i})$

  3. The x-component  of electric field at $(1, 0, 2)$ is $(-8\hat{i})$

  4. The y-and z-components of the field are constant in magnitude.


Correct Option: A,B,C,D
Explanation:
We have $V = 4x^2$
So, the $x , y$ and $z$ components of the electrostatic field are

$E _x = \dfrac{-\partial V}{\partial x} = -8x$

$E _y = \dfrac{-\partial V}{\partial y} = 0$

$E _z = \dfrac{-\partial V}{\partial z} = 0$

So, $\overrightarrow{E} = E _x\hat{i} + E _y \hat{j} + E _z\hat{k} = -8x\hat{i}$. 
The electrostatic field at $(1, 0, 2)$ is $\overrightarrow{E} = (-8)\hat{i} \,V/m$.

Two conducting shells of radii $2\ cm$ and $3\ cm$ are separately charged by $10\ V$ and $5\ V$ potential, respectively. Now smaller shell is placed inside bigger shell, and  then connected by a wire. What will be potential at the surface of smaller shell ?

  1. zero

  2. $\dfrac{35}{3}\ volt$

  3. $\dfrac{25}{3}\ volt$

  4. $\dfrac{10}{3}\ volt$


Correct Option: C

If on the x-axis electric potential decreases uniformly from 60 V to 20 V between x = -2 m to x = +2 m, then the magnitude of electric field at the origin

  1. Must be 10 V/m

  2. May be greater than 10 V/m

  3. Is zero

  4. Is 5 V/m


Correct Option: A

$64$ charged drops coalesce to form a bigger charged drop. The potential of bigger drop will be times that of smaller drop-

  1. $4$

  2. $16$

  3. $64$

  4. $8$


Correct Option: B

A uniform electric field $10N/C$ exists in the vertically downward direction, the increase in the electric potential as one goes through a height of $50cm$ is:

  1. $20J$

  2. $\dfrac{1}{5}J$

  3. $5J$

  4. $\dfrac{1}{20}J$


Correct Option: A
Explanation:
Electric field $=10N/C$
Vertically downward direction electric potential as one goes through $h=50cm$ $=50\times { 10 }^{ -2 }m$
Now, $V=E/d$
$=10/50\times { 10 }^{ -2 }=\dfrac { 100 }{ 5 } =20J$

In an electric field the potential at a point is given by the following relation $V = \dfrac{343}{r}$ where r is distance from the origin. The electric field at $r = 3\hat i + 2\hat j + 6\hat k $ is:

  1. $21\hat i + 14\hat j + 42\hat k $

  2. $3\hat i + 2\hat j + 6\hat k $

  3. $\dfrac{1}{7}(3\hat i + 2\hat j + 6\hat k )$

  4. $-(3\hat i + 2\hat j + 6\hat k )$


Correct Option: D
Explanation:

B. $3i+2j+6k$


Formula,

$E=\dfrac{V}{|\vec{r}|}\cdot \hat{r}$

$E=\dfrac{343}{|\vec{r}|^2}\cdot \dfrac{3i+2j+6k}{|r|}$

$=\dfrac{343}{7^2}\cdot \dfrac{3i+2j+6k}{7}$

$=3i+2j+6k$

The electric field in a region is directed outward and is proportional to the distance r from the origin. Taking the electric potential at the origin to be zero, the electric potential at a distance r?

  1. Is uniform in the region

  2. Is proportional to r

  3. Is proportional to $r^2$

  4. Increases as one goes away from the origin


Correct Option: C
Explanation:

$\quad E∝r\quad and\quad V=0\quad at\quad r=0$

$E=kr$
$E=\frac { -dv }{ dr } $
$V=-int{Edr}$
$V=-int { Krdr}$ 
$V=-k\frac { { r }^{ 2 } }{ 2 } +C$
$V=-k\frac { { r }^{ 2 } }{ 2 } $
$V=0\quad r=0\quad C=0$
$V=0\quad r=0\quad C=0$
 v is proportional to ${ r }^{ 2 }$

In a certain region of space, the potential is given by $V=k\left[ { 2x }^{ 2 }-{ y }^{ 2 }+{ z }^{ 2 } \right] $. The electric field at the point$ (1,1,1)$ has magnitude :

  1. $k\sqrt { 6 } $

  2. $2k\sqrt { 6 } $

  3. $2k\sqrt { 3 } $

  4. $4k\sqrt { 3 } $


Correct Option: B
Explanation:

Given, $V=k[2x^2-y^2+z^2]$

Electric field , $\vec{E}=-(\dfrac{dV}{dx}\hat i+\dfrac{dV}{dy}\hat j+\dfrac{dV}{dz}\hat {k})$

or,$\vec{E}=-k(4x\hat i-2y\hat j+2z\hat k)$

or,$\vec{E} _{(1,1,1)}=-k(4\hat i-2\hat j+2\hat k)$

Magnitude of electric field$ =|\vec{E} _{(1,1,1)}|=\sqrt{k^2(16+4+4)}=k\sqrt {24}=2k\sqrt 6$

Let V be electric potential and E the magnitude of the electric field. At a given position, which of the statement is true

  1. E is always zero where V is zero

  2. V is always zero where E is zero

  3. E can b zero where V is non zero

  4. E is always nonzero where V is nonzero


Correct Option: A

Two plates are 1 cm apart and the potential difference between them is 10 volt. The electric field between the plates is

  1. 10 N/C

  2. 250 N/C

  3. 500 N/C

  4. 1000 N/C


Correct Option: D