Tag: field strength and potential gradient

Questions Related to field strength and potential gradient

The potential at a point $x$ (measured in $\mu m )$ due to somecharges situated on the $x$ -axis is given by $V ( x ) = 20 / \left( x ^ { 2 } - 4 \right)$Volts. The electric field $E$ at $x = 4 \mu m$ is given by

physics coulomb's law field strength and potential gradient electric field as gradient of potential relation between electric field and electric potential

  1. 5$/ 3$ Volt / \mum and in the -ve $x$ direction

  2. 5$/ 3$ Volt $/ \mu m$ and in the +ve $x$ direction

  3. 10$/ 9$ Volt / \mum and in the -ve $x$ direction

  4. 10$/ 9$ Volt $/ \mu m$ and in the +ve $x$ direction

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Correct Option: B

Variation in potential is maximum if one goes :

physics coulomb's law field strength and potential gradient electric field as gradient of potential relation between electric field and electric potential

  1. along the line of force

  2. perpendicular to the line of force

  3. in any direction

  4. none of these

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Correct Option: A
Explanation:

$dV=-\vec{E}.d\vec{r}=-Edr cos\theta$


Hence, variation will be maximimum for $\theta=0^{o}$ or $180^{o}$, that is variation $dV$ is maximum along line of field or say line of force.

Answer-(A)

The electric field lines are closer together near object $A$ than they are near object $B$. We can conclude that :

physics coulomb's law field strength and potential gradient electric field as gradient of potential relation between electric field and electric potential

  1. the potential near $A$ is greater than the potential near $B$

  2. the potential near $A$ is less than the potential near $B$

  3. the potential near $A$ is equal to the potential near $B$

  4. nothing about the relative potentials near $A$ and $B$

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Correct Option: D
Explanation:

Potential decreases in the direction of electric field. So it depends  on whether the lines of forces are from $A$ to $B$ or from $B$ to $A$.

There is an electric field $E$ in the x-direction. If the work done by the electric field in moving a charge of $0.2 C$ through a distance of $2 m$ along a line making an angle $60^{\circ}$ with the x-axis is $4 J$, then what is the value of $E$?

physics coulomb's law field strength and potential gradient electric field as gradient of potential relation between electric field and electric potential

  1. $\displaystyle \sqrt3 NC^{-1}$

  2. $\displaystyle 4 NC^{-1}$

  3. $\displaystyle 5 NC^{-1}$

  4. $\displaystyle 20 NC^{-1}$

Show answer
Correct Option: D
Explanation:

$\displaystyle F = qE$
work will only be done in moving the charged particle in $x$ direction

work done in moving the charge in y-direction will be $0$
Work done , $W=\int \vec{F}.\vec{dr}$

$\displaystyle W = qE \times 2 cos  60^{\circ}$

or $\displaystyle 4 = 0.2E\times 2 \times \dfrac{1}{2}$

$  \implies  E = 20 NC^{-1}$

Charge $Q$ is given a displacement $\displaystyle \vec{r} = a\hat{i}+b\hat{j}$ in an electric field $\displaystyle \vec{E} = E _1\hat{i}+E _2\hat{j}$. The work done is :

physics coulomb's law field strength and potential gradient electric field as gradient of potential relation between electric field and electric potential

  1. $\displaystyle Q(E _1a+E _2b)$

  2. $\displaystyle Q\sqrt{(E _1a)^2+(E _2b)^2}$

  3. $\displaystyle Q (E _1+E _2) \sqrt{a^2+b^2}$

  4. $\displaystyle Q \sqrt{(E _1^2+E^2 _2)^2} \sqrt{a^2+b^2}$

Show answer
Correct Option: A
Explanation:

Work done in the presence of electric field E is $W=\vec F. \vec r = q\vec E.\vec r$
$W=Q[(E _1\hat{i}+E _2\hat{j}).( a\hat{i}+b\hat{j})]$
$W=Q(E _1a+E _2b)$

The electric potential decreases uniformly from $120V$ to $80V$ as one moves on the x-axis from $x=-1cm$ to $x=+1cm$. The electric field at the origin

physics coulomb's law field strength and potential gradient electric field as gradient of potential relation between electric field and electric potential

  1. must be equal to $20V{cm}^{-1}$

  2. may be equal to $20V{cm}^{-1}$

  3. may be greater than $20V{cm}^{-1}$

  4. may be less than $20V{cm}^{-1}$

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Correct Option: B,C

The electric potential decreases uniformly from 120 V to 80 V as one moves on the x-axis from $x = -1\ cm$ to $ x = +1 \ cm$. The electric field at the origin.

physics coulomb's law field strength and potential gradient electric field as gradient of potential relation between electric field and electric potential

  1. must be equal to 20 Vcm$^{-1}$

  2. must be equal to 20 Vm$^{-1}$

  3. greater than or equal to 20 Vcm$^{-1}$

  4. may be less than 20 Vcm$^{-1}$

Show answer
Correct Option: A,C
Explanation:

$dv=-\vec E.\vec dx=-E dx \cos\theta$

$\displaystyle E = -\dfrac{dV}{\cos\theta dx} $

$\cos\theta\approx 1$, if we take $\cos\theta =1$,then

$E _{min}= -\dfrac{80-120}{1-(-1)} =\dfrac{40}{2}= 20 V cm^{-1}$

Hence E would be greater than or equal to $20$

Mark the correct statement:

physics coulomb's law field strength and potential gradient electric field as gradient of potential relation between electric field and electric potential

  1. If $E$ is zero at a certain point, then $V$ should be zero at that point

  2. If $E$ is not zero at a certain point, then $V$ should not be zero at that point

  3. If $V$ is zero at a certain point, then $E$ should be zero at that point

  4. If $V$ is zero at a certain point, then $E$ may or maynot be zero

Show answer
Correct Option: D
Explanation:

Since $E=\dfrac{-dV}{dr}$

A zero potential at a point never means that the electric field is also zero at a point always.
$E=0$ when $V=$ constant.
If $V=0$; then $E$ may or may not be zero.
Similarly, if $E=0$; then $V$ must either be a constant or may be zero.
so correct option is(d).

For a uniform electric field $\vec{E}=E _{0}(\hat{i})$, if the electric potential at x=0 is zero, then the value of electric potential at x=+x will be .......

physics coulomb's law field strength and potential gradient electric field as gradient of potential relation between electric field and electric potential

  1. $xE _{0}$

  2. -$xE _{0}$

  3. $x^{2}E _{0}$

  4. -$x^{2}E _{0}$

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Correct Option: B

The potential $V$ is varying with x and y as $\displaystyle V = \dfrac{1}{2}(y^2-4x)$ volt. The field at $x = 1 m , y = 1 m$, is :

physics coulomb's law field strength and potential gradient electric field as gradient of potential relation between electric field and electric potential

  1. $\displaystyle 2\hat{i}+\hat{j} \ Vm^{-1}$

  2. $\displaystyle -2\hat{i}+\hat{j} \ Vm^{-1}$

  3. $\displaystyle 2\hat{i}-\hat{j} \ Vm^{-1}$

  4. $\displaystyle -2\hat{i}+2\hat{j} \ Vm^{-1}$

Show answer
Correct Option: C
Explanation:

$\displaystyle E _x = -\dfrac{dV}{dx} = -\dfrac{1}{2} [-4] = 2$

 $\displaystyle E _y = -\dfrac{dV}{dy} = -\dfrac{1}{2}[2y] = - y = -1$

 $\displaystyle \therefore \vec {E} = E _x \hat{i}+E _y \hat{j}=2\hat{i}-1\hat{j}$