Tag: potential energy of a system of charges

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

Calculate the electrostatic potential energy of two electrons separated bt 3 $\overset { \circ  }{ A } $ in vacuum

  1. $7.69\times10^{-19} J$

  2. $8.69\times10^{-19} J$

  3. $5.69\times10^{-19} J$

  4. $6.69\times10^{-19} J$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

U = k * q1 * q2 / r. k = 9 * 10^9, q = 1.6 * 10^-19 C, r = 3 * 10^-10 m. U = (9 * 10^9 * (1.6 * 10^-19)^2) / (3 * 10^-10) = 7.68 * 10^-19 J. Option B is the closest value provided.

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

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?

  1. They have different speeds

  2. They have same momentum

  3. They have same kinetic energy

  4. They have been subjected to same force
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Kinetic energy gained is q * V. Since both particles have the same charge q and are accelerated through the same potential V, they gain the same kinetic energy. Therefore, the statement that they have different kinetic energies is false.

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                         $\Delta U=kq^{2}\left(1/3r-1/2r\right)=-kq^{2}/6r$