Tag: electrostatics

Quizzes (15) Questions (156)

Questions Related to electrostatics

Multiple choice potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

A flat circular fixed disc has a charge +Q uniformly distributed on the disc. A charge +q is thrown with kinetic energy K,towards the disc along its axis The charge is q

  1. will not hit the disc at the center

  2. may return back along its path after touching the disc

  3. may return back along its path without touching the disc

  4. any of the above three situation is possible depending on the magnitude of K
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The electric field of a uniformly charged disc along its axis is directed away from the disc. A positive charge q approaching the disc will experience a repulsive force, causing it to decelerate and potentially return before reaching the disc.

Multiple choice potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

Particle A having positive charge is moving directly head on towards initially stationary positively charged particle B. At the instant when A and B are closest together. 

  1. the momenta of A and B must be equal

  2. the velocities of A and B must be equal

  3. B would have gained less kinetic energy than A would have lost

  4. B would have gained the same momentum as A would have lost
Reveal answer Fill a bubble to check yourself
C,D Correct answer
Multiple choice potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

Eight charges (each $q$) are placed at the vertices of a regular cube of side $a$. The electric potential energy of the configuration will be $ U=12\times \dfrac { 1 }{ 4\pi \varepsilon _{ 0 } } ,\dfrac { q^{ 2 } }{ a } \times \quad x $ then x.

  1. $ 1+\dfrac { 1 }{ \sqrt { 2 } } +\dfrac { 1 }{ \sqrt { 3 } } $
  2. $ 1+\dfrac { 2 }{ \sqrt { 2 } } +\dfrac { 1 }{ \sqrt { 3 } } $
  3. $ 1+\dfrac { 2 }{ \sqrt { 2 } } +\dfrac { 2 }{ \sqrt { 3 } } $
  4. $ \left[ 1+\dfrac { 1 }{ \sqrt { 2 } } +\dfrac { 1 }{ 3\sqrt { 3 } } \right] $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total potential energy of a cube of 8 charges is the sum of interactions: 12 edges (distance a), 12 face diagonals (distance a*sqrt(2)), and 4 body diagonals (distance a*sqrt(3)). Summing these gives U = (q^2 / (4*pi*e0*a)) * (12 + 12/sqrt(2) + 4/sqrt(3)). Factoring out 12 gives the expression in option D.

Multiple choice potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

Two point charges of +10 $\mu c$ and -10 $\mu c$ are placed at a distance $40$ cm in air. Potential energy of the system will be-

  1. $2.25 J$
  2. $2.35 J$
  3. $-2.25 J$
  4. $-2.35 J$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

U = k * q1 * q2 / r. k = 9 * 10^9, q1 = 10^-5 C, q2 = -10^-5 C, r = 0.4 m. U = (9 * 10^9 * -10^-10) / 0.4 = -0.9 / 0.4 = -2.25 J.

Multiple choice potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

A solid non-conducting sphere of radius $R$ having charge density $\rho = \rho _{0}x$, where $x$ is distance from the centre of sphere. The self potential energy of the sphere is

  1. $\dfrac {\pi \rho _{0}^{2} R^{4}}{6\epsilon _{0}}$
  2. $\dfrac {\pi \rho _{0}^{2} R^{6}}{4\epsilon _{0}}$
  3. $\dfrac {\pi \rho _{0}^{2} R^{6}}{6\epsilon _{0}}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The self-potential energy of a sphere with non-uniform charge density is found by integrating the energy density or using the potential at each shell. For rho = rho0 * x, the integration leads to the result in option C.

Multiple choice potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

If a proton and an electron are accelerated through the same potential difference:

  1. both the proton and electron have same K.E

  2. both the proton and electron have same momentum

  3. both the proton and electron have same velocity

  4. both the proton and electron have same temperature
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P.D = V
K.E = eV
Velocity will be equal and opposite

Multiple choice potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

What is the change in potential energy of a particle of charge +q that is brought from a distance of 3r to a distance of 2r by a particle of charge q? 

  1. $kq^2/r$
  2. $-kq^2/6r$
  3. $kq^2/r^2$
  4. $-kq^2//4r^2$
  5. $8kq^2/r^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

As the $+q$ is brought near by charge $q$ so there is an attraction force it means q is a negative charge, equal to $-q$.
 The electric potential energy of a system of two point charges (  $+q$ ,  $-q$) sepatrated by a distance $3r$ is given by ,
                  $U=k\dfrac{q\times -q}{3r}$  , 
when the separation is reduced to $2r$ then potential energy will become ,
                 $U'=k\dfrac{q\times- q}{2r}$ 
therefore change in potential energy is 
                             $\Delta U=U'-U$ 
or                         $\Delta U=-k\dfrac{q\times q}{2r}+k\dfrac{q\times q}{3r}$
or                         $\Delta U=kq^{2}\left(1/3r-1/2r\right)=-kq^{2}/6r$

Multiple choice potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

The ratio of momentum of an electron and an alpha particle which are accelerated from rest by  potential difference of 100 V is:

  1. $\sqrt{\dfrac{m _{\alpha}}{m _e}}$
  2. $\sqrt{\dfrac{m _e}{m _{\alpha}}}$
  3. $\dfrac{2m _e}{m _{\alpha}}$
  4. $\sqrt{\dfrac{m _e}{2m _{\alpha}}}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Mass of proton $=1$ $u$

and, Mass of alpha particle $=4$ $u$
Charge of proton $=e$
And, charge of alpha particle $=2e$
For charge moving in a uniform potential field.
$K.E=$ Electric potential energy
$\cfrac{1}{2}mv^2=qV$
$v=\sqrt{\cfrac{2qV}{m}}$
OR,
Momentum $(P)=mv$
$\Rightarrow P=m\sqrt{\cfrac{2qV}{m}}$
$\Rightarrow P=\sqrt{m2qV}$
Momentum of proton,
$P _1=\sqrt{2qVm _1}=\sqrt{2eVm _e}$
Momentum of alpha particle 
$P _2=\sqrt{2qVm _2}=\sqrt{2\times 2eVm _a}$
$\therefore \cfrac{P _1}{P _2}=\sqrt{\cfrac{2eVm _e}{4eVm _a}}$
$\therefore \cfrac{P _1}{P _2}=\sqrt{\cfrac{m _e}{2m _a}}$

Multiple choice potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

A sphere of radius $1$ cm has potential of $8000$V. The energy density near the surface of sphere will be?

  1. $64\times 10^5$ $J/m^3$
  2. $8\times 10^3$ $J/m^3$
  3. $32$ $J/m^3$
  4. $2.83$ $J/m^3$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Energy density = $=(\frac { 1 }{ 2 } )∈0E2$ 
$=(\frac { 1 }{ 2 } )\times 8.86\times 10-12\times \left( \frac { v }{ r }  \right) 2$
$=4.43\times 10-12\times [(8000)/(10-2)]2$
$=283.5\times 10-2$
$=2.83J/m3$
Multiple choice potential energy of a system of charges potential energy of various configurations electrostatic potential and capacitance electrostatics physics

Two unlike charges of magnitude q are separated by a distance 2d. The potential at a point midway between them is

  1. zero
  2. $\dfrac{1}{4 \pi {\epsilon} _{0}}$
  3. $\dfrac{1}{4 \pi {\epsilon} _{0}}$ . $\dfrac{q}{d}$
  4. $\dfrac{1}{4 \pi {\epsilon} _{0}}$ . $\dfrac{2q}{d}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The potential at a point midway between two equal and opposite charges is the sum of the potentials from each: V = k * q / d + k * (-q) / d = 0.