Tag: physics

Questions Related to physics

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 :

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

  1. $0$

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

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

  4. $\dfrac{-6\phi _0}{\varepsilon _0}$

Show answer
Correct Option: B
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 $

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:

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

  1. 3

  2. 4

  3. 5

  4. 6

Show answer
Correct Option: A
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$=|W|=3$

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

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

  1. $5.20\ N$

  2. $7.20\ N$

  3. $6.20\ N$

  4. $8.20\ N$

Show answer
Correct Option: B
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)

The most appropriate relationship between electric field and electric potential 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. $E = - \nabla V _E$

  2. $V _E = - \nabla E$

  3. $E = \nabla V _E$

  4. $V = - \nabla E$

Show answer
Correct Option: A
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)

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

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

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

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

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

  4. $5.4 \times {10^6}J$

Show answer
Correct Option: A
Explanation:

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

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

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 :

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

  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

Show answer
Correct Option: B
Explanation:

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

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

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

  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.

Show answer
Correct Option: C
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 .

The frequency of ac mains in India is:

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

  1. $30$ Hz

  2. $50$ Hz

  3. $60$ Hz

  4. $120$ Hz

Show answer
Correct Option: B
Explanation:

Frequency of AC mains in India is 50 Hz,similar to most European countries. Whereas USA uses 60 Hz

Various distribution circuits are connected in

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

  1. series

  2. parallel

  3. series or parallel

  4. nothing can be decided

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Correct Option: B
Explanation:

Parallel circuit configuration limits the amount of power in each circuit and if one circuit breaker goes out, power remains on in the rest of the home.

Which of the following can be true?

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

  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.

Show answer
Correct Option: A