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

If the electrostatic potential is given by $\phi =\phi _0(x^2+ y^2 + z^2)$ where $\phi _0$ is constant, then the charge density of the given potential would be :

  1. $0$

  2. $-6\phi _0\varepsilon _0$

  3. $-2\phi _0\varepsilon _0$

  4. $\dfrac{-6\phi _0}{\varepsilon _0}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$ \overrightarrow{E} = -\triangledown \phi $
$ \overrightarrow{\triangledown}.\overrightarrow{E} = \rho/\epsilon _0 $
Now, $\phi = \phi _0 (x^2 + y^2 + z^2) \Rightarrow \overrightarrow{E} = -2\phi _0 ( \hat{i}+\hat{j}+\hat{k} ) \Rightarrow \rho = -6\phi _0 \epsilon _0 $

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

Electric field in a region is given as $\bar{E}=x\hat{i}+2y\hat{j}+3\hat{k}$. In this region point A(3,3,1) and point B (4,2,1) are there. The magnitude of work done by the electric field, if 2 coulomb charge is moved from A to B. All values are in SI units:

  1. 3

  2. 4

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given, $\vec{E}=x\hat{i}+2y\hat{j}+3\hat{k}$ and $ q=2 C$
Work done, $W=\int^B _Aq\vec{E}.\vec{dr}=q\int^B _A(x\hat{i}+2y\hat{j}+3\hat{k}).(dx\hat{i}+dy\hat{j}+dz\hat{k})$
or,$W=2\int^{(4,2,1)} _{(3,3,1)}xdx+2ydy+3dz=2[\frac{16-9}{2}+(4-9)+3(1-1)]=7-10=-3$
Magnitude of work done$=|W|=3$

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

Find the magnitude of the force on a charge of $12\mu C$ placed at point where the potential gradient has a magnitude of $6\times 10^{5}V\ m^{-1}$

  1. <span>$5.20\ N$</span>

  2. <span>$7.20\ N$</span>

  3. <span>$6.20\ N$</span>

  4. <span>$8.20\ N$</span>
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Potential gradient is nothing but the rate of change of electric potential with position and it is equal to electric field at that point.


$\dfrac{dV}{dl}=E$=electric field

$\implies E=6\times 10^5Vm^{-1}$

Force on charge $=F=qE=12\times 10^{-6}\times 6\times 10^5$

$\implies F=7.2N$

Answer-(B)

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

The most appropriate relationship between electric field and electric potential is given by

  1. $E = - \nabla V _E$

  2. $V _E = - \nabla E$

  3. $E = \nabla V _E$

  4. $V = - \nabla E$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\vec{E}=-\dfrac{\partial V}{dx}\hat{i}-\dfrac{\partial V}{dy}\hat {j}-\dfrac{\partial V}{dz}\hat{k}$


And, we know that $\nabla=\dfrac{\partial}{dx}+\dfrac{\partial}{dy}+\dfrac{\partial}{dz}$

Hence, we get $\vec{E}=-\nabla V$

Answer-(A)

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

Electrostatic potential energy of a shell of radius $10cm.$ When $10C$ charge is distributed over its surface.

  1. $4.5 \times {10^{12}}J$

  2. $5.4 \times {10^8}J$

  3. $4.5 \times {10^9}J$

  4. $5.4 \times {10^6}J$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$U = \dfrac{{k\,Q \cdot Q}}{{2R}}$

    $ = \dfrac{{9 \times {{10}^9} \times 10 \times 10}}{{2 \times 0.1}}$
$U = 4.5 \times {10^{12}}J$

Multiple choice physics electrostatics field strength and potential gradient electric field as gradient of potential relation between electric field and electric potential

Two charges $+Q$ and $-2Q$ are located at points $A$ and $B$ on a horizontal line as shown in the diagram.
The electrical field is zero at a point which is located at finite distance :

  1. On the perpendicular bisector of $AB$

  2. Left of $A$ on the line

  3. Between $A$ and $B$ on the line

  4. Right of $B$ on the line
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$ E _1 $ = Electrical field due to $+Q$
$E _2$ = Electrical feild due to $-2Q$
There resultant is $0$ at this point 

Multiple choice physics electrical circuits domestic electric circuits and safety precautions domestic and commercial circuit electric power

Alternating current can not be measured by $D.C$. ammeter because 

  1. $A.C$. cannot pass through $D.C$.

  2. $A.C$. changes direction

  3. average value of current for complete cycle is zero

  4. $D.C$. ammeter will get damaged.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

While for half-circle, the value of current is different at different points and for complete cycle its average value is zero.

So, we can't measure current by $D.C$ ammeter .

Multiple choice physics electrical circuits domestic electric circuits and safety precautions domestic and commercial circuit electric power

Which of the following can be true?

  1. The instantaneous power output of an ac source can be negative.

  2. The average power output of an ac source can be negative.

  3. The instantaneous power output of an ac source can NOT be negative.

  4. The average power output of an ac source can NOT be negative.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In an AC circuit, the instantaneous power p = v*i can be negative if the voltage and current have opposite signs, which occurs when the phase difference is between 90 and 270 degrees.