Potential energy of various configurations - class-XII
potential energy of various configurations
Questions
Two thin wire rings each having a radius R are placed at a distance d apart with their axes coinciding . The charges on the two rings are + q and -q . The potential difference between the centres of the two rings is
- $\frac {{ Q.R }\quad} {\quad { 4\pi }{ \varepsilon } _{ 0 }{ d }^{ 2 }}$
- $\frac { Q }{ 2\pi { \varepsilon } _{ 0 } } [\frac { 1 }{ R } -\frac { 1 }{ \sqrt { { R }^{ 2 }+{ d }^{ 2 } } } ]$
- $\frac { Q }{ { 4\pi \varepsilon } _{ 0 } } [\frac { 1 }{ R } -\frac { 1 }{ \sqrt { { { R }^{ 2 } }+{ { d }^{ 2 } } } } ]$
- 0
what is the potential difference between two points, if 2J of work must be done to move a 4 mC charge from one point to another is:
- 50 V
- 500 V
- 5 V
- 5000 V
A point charge q is rotated along a circle in the electric field generated by another point charge Q. The work done by the electric field on the rotating charge in one complete revolution is_______
- zero
- positive
- negative
- zero if the charge Q is at the center and nonzero otherwise.
$100J$ of work is done when $2 \mu C$ charge is moved in an electric field between two points. The p.d. between the points is
- $2\times10^{-4}V$
- $2\times10^{-8}V$
- $2\times10^{-6}V$
- $5\times10^{7}V$
A hollow metal sphere of radius $5\ cm$ is charged such that the potential on its surface is $10$ volts. The potential of the centre of the sphere is:
- zero
- $10$ volts
- Same as at a point $5\ cm$ away from the surface.
- Same as at a point $25\ cm$ away from the surface.
A spherical shell of radius $R _1$ with uniform charge $q$ is expanded to a radius $R _2$. Find the work performed by the electric forces during the shell expansion from $R _1$ to radius $R _2$.
- $\dfrac{q^2}{2\pi in _0}\left(\dfrac{1}{R _1} - \dfrac{1}{R _2}\right)$
- $\dfrac{q^2}{3\pi in _0}\left(\dfrac{1}{R _1} - \dfrac{1}{R _2}\right)$
- $\dfrac{q^2}{5\pi in _0}\left(\dfrac{1}{R _1} - \dfrac{1}{R _2}\right)$
- $\dfrac{q^2}{8\pi in _0}\left(\dfrac{1}{R _1} - \dfrac{1}{R _2}\right)$
Two insulated charged spheres of radii ${R} _{1}$ and ${R} _{2}$ having charges ${Q} _{1}$ and ${Q} _{2}$ respectively are connected to each other, then there is:
- no change in the energy of the sytem
- an increase in the energy of the system
- always a decrease in the energy of the system
- a decrease in energy of the system unless ${q} _{1}{R} _{2}={q} _{2}{R} _{1}$
Two small spheres have mass ${m} _{1}$ and ${m} _{2}$ and hanging from massless insulating threads of lengths ${l} _{1}$ and ${l} _{2}$. Two spheres carry charges ${q} _{1}$ and ${q} _{2}$ respectively. The spheres hang such that they are on the same horizontal level and the threads are inclined to the vertical at angle ${\theta} _{1}$ and ${\theta} _{2}$ respectively. If $F _1 = F _2$, then:
- ${ \theta } _{ 1 }={ \theta } _{ 2 }$
- ${ M } _{ 1 }={ M } _{ 2 }$
- $\cfrac { l _{ 1 } }{ \tan { { \theta } _{ 1 } } } =\cfrac { l _{ 2 } }{ \tan { { \theta } _{ 2 } } } \quad $
- $\cfrac { q _{ 1 } }{ \tan { { \theta } _{ 1 } } } =\cfrac { q _{ 2 } }{ \tan { { \theta } _{ 2 } } } $
Two particles $X$ and $Y$ having equal charges after being accelerated thorough the same potential difference enter a region of uniform magnetic field and describe circular paths of radius $R _1$ and $R _2$ respectively. the ratio of mass of $X$ to that of $Y$ is
- $\sqrt { R _1{/R _2} }$
- $R _2{/R _1}$
- $(R _1{/R _2})^2$
- $R _1{/R _2}$
An electron in a picture tube of TV set is accelerated from rest through a potential difference of $5\times 10^3V$.Then the speed of electron as a result of acceleration is going to be
- $1.2 \times 10^7m/s$
- $2.2\times 10^7m/s$
- $3.2 \times 10^7m/s$
- $4.2\times 10^7m/s$.
A charge $10$ esu is placed at a distance of $2$ cm, from a charge$ 40$ esu and $4$ cm. from another charge -$20$ esu. The potential energy of the charge $10$ esu is :- (In ergs)
- $87.5$
- $112.5$
- $150$
- $zero$
Calculate the electrostatic potential energy of two electrons separated bt 3 $\overset { \circ }{ A } $ in vacuum
- $7.69\times10^{-19} J$
- $8.69\times10^{-19} J$
- $5.69\times10^{-19} J$
- $6.69\times10^{-19} J$
A proton and a deuteron are initialy at rest an dare accelerated through the same potential difference. Which following is false concerning the final properties of the two particles?
- They have different speeds
- They have same momentum
- They have same kinetic energy
- They have been subjected to same force
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
- will not hit the disc at the center
- may return back along its path after touching the disc
- may return back along its path without touching the disc
- any of the above three situation is possible depending on the magnitude of K
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.
- the momenta of A and B must be equal
- the velocities of A and B must be equal
- B would have gained less kinetic energy than A would have lost
- B would have gained the same momentum as A would have lost
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+\dfrac { 1 }{ \sqrt { 2 } } +\dfrac { 1 }{ \sqrt { 3 } } $
- $ 1+\dfrac { 2 }{ \sqrt { 2 } } +\dfrac { 1 }{ \sqrt { 3 } } $
- $ 1+\dfrac { 2 }{ \sqrt { 2 } } +\dfrac { 2 }{ \sqrt { 3 } } $
- $ \left[ 1+\dfrac { 1 }{ \sqrt { 2 } } +\dfrac { 1 }{ 3\sqrt { 3 } } \right] $
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-
- $2.25 J$
- $2.35 J$
- $-2.25 J$
- $-2.35 J$
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
- $\dfrac {\pi \rho _{0}^{2} R^{4}}{6\epsilon _{0}}$
- $\dfrac {\pi \rho _{0}^{2} R^{6}}{4\epsilon _{0}}$
- $\dfrac {\pi \rho _{0}^{2} R^{6}}{6\epsilon _{0}}$
- None of these
If a proton and an electron are accelerated through the same potential difference:
- both the proton and electron have same K.E
- both the proton and electron have same momentum
- both the proton and electron have same velocity
- both the proton and electron have same temperature
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?
- $kq^2/r$
- $-kq^2/6r$
- $kq^2/r^2$
- $-kq^2//4r^2$
- $8kq^2/r^2$
The ratio of momentum of an electron and an alpha particle which are accelerated from rest by potential difference of 100 V is:
- $\sqrt{\dfrac{m _{\alpha}}{m _e}}$
- $\sqrt{\dfrac{m _e}{m _{\alpha}}}$
- $\dfrac{2m _e}{m _{\alpha}}$
- $\sqrt{\dfrac{m _e}{2m _{\alpha}}}$
A sphere of radius $1$ cm has potential of $8000$V. The energy density near the surface of sphere will be?
- $64\times 10^5$ $J/m^3$
- $8\times 10^3$ $J/m^3$
- $32$ $J/m^3$
- $2.83$ $J/m^3$
Two unlike charges of magnitude q are separated by a distance 2d. The potential at a point midway between them is
- zero
- $\dfrac{1}{4 \pi {\epsilon} _{0}}$
- $\dfrac{1}{4 \pi {\epsilon} _{0}}$ . $\dfrac{q}{d}$
- $\dfrac{1}{4 \pi {\epsilon} _{0}}$ . $\dfrac{2q}{d}$
The potential in certain region is given as $V = 2x^2$, then the charge density of that region is
- $-\dfrac{4x}{\varepsilon _0}$
- $-\dfrac{4}{\varepsilon _0}$
- $-4 \varepsilon _0$
- $-2 \varepsilon _0$
A particle A has charge +q and a particle B has a charge +9q with each of them having the same mass m.If both the particles are allowed to all from rest through the same potential difference, then the ratio of their speed is
- $1:2$
- $1:\sqrt 3$
- $1:2\sqrt { 2 } $
- none of these
Positive charge Q is uniformly distributed throughout the volume of a dielectric sphere of radius R. A point mass having charge +q and mass m is fired towards the centre of the sphere with velocity v from a point A at distance r(r> R) from the centre of the sphere. Find the minimum velocity v so that it can penetrate R/2 distance of the sphere. Neglect any resistance other than electric interaction. Charge on the small mass remains constant throughout the motion.
- <span>$\displaystyle \left[\frac{1}{2 \pi \varepsilon _0} \frac{Qq}{Rm} \left(\frac{r-R}{r} + \frac{3}{4}\right) \right]^{1/2}$</span>
- <span>$\displaystyle \left[\frac{1}{2 \pi \varepsilon _0} \frac{Qq}{Rm} \left(\frac{r-R}{r} + \frac{3}{8}\right) \right]^{1/2}$</span>
- <span>$\displaystyle \left[\frac{1}{2 \pi \varepsilon _0} \frac{Qq}{Rm} \left(\frac{r-R}{r} - \frac{3}{8}\right) \right]^{1/2}$</span>
- <span>$\displaystyle \left[\frac{1}{4 \pi \varepsilon _0} \frac{Qq}{Rm} \left(\frac{r-R}{r} + \frac{3}{4}\right) \right]^{1/2}$</span>
A particle of mass $10^{-3}kg$ and charge $5\mu C$ is thrown at a speed $20\ m\ s^{-1}$ against a uniform electric field of strength $2\times 10^{5}N\ C^{-1}$. How much distance will it travel before coming to rest momentarily?
- <span>$0.1\ m$</span>
- <span>$0.3\ m$</span>
- <span>$0.05\ m$</span>
- <span>$0.2\ m$</span>
The electric potential energy of a uniformly charged thin spherical shell of radius 'R' having a total charge 'Q' is
- $\dfrac{KQ^2}{4R}$
- $\dfrac{KQ^2}{6R}$
- $\dfrac{KQ^2}{8R}$
- $\dfrac{KQ^2}{16R}$
A uniform electric field of magnitude $290 V/m$ is directed in the positive $x$ direction. A $+13.0 \mu C$ charge moves from the origin to the point $(x, y) = (20.0 cm, 50.0 cm).$
What is the change in the potential energy of the charge field system?
- $-754J$
- $-754mJ$
- $-754kJ$
- $-754\mu J$