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Byju's Answer

Standard XII

Physics

The Self Potential Energy of Continuous Charge Distributions

You are movin...

Question

You are moving a negative charge -q, where -q<0 at a small constant speed away from a uniformly charged non-conducting spherical shell on which resides a negative charge -Q<0. The electrostatic field of -Q is E. Let U be the total energy of the system, $W_{a}$ is the work done by the force $F_{a}$ you exert on -q and $W_{E}$ the work done by the electrostatic force $F_{E}$ on -q. Then, as -q is being moved

W_{a} = - W_{E}

, therefore U remains constant

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F_{a} = - F_{E}

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U increases

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U decreases

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Solution

The correct option is D U decreases

If charge is being moved slowly, $_{a} = -_{E}$
$W_{a} + W_{E} = Δ K E = 0$ [Charge is moved slowly at constant speed]
i.e., $W_{a} = - W_{E}$
Also $W_{E} = - Δ U$
Thus, $W_{a} = + Δ U$
As force $F_{a}$ and displacement are $180^{\circ}$
$\to F . \to d r < 0$
$W_{a} < 0$
Thus, $Δ U < 0$
therefore, U decreases.

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Similar questions

Q. You are moving a negative charge

q < 0

at a small constant speed away from a uniformly charged non-conducting spherical shell on which resides a negative charge

Q < 0

. The electrostatic field of

Q

E

. Let

U

be the total energy of the system,

W_{a}

the work done by the force

F_{a}

you exert on

q

and

W_{E}

the work done by the electrostatic force

F_{E}

q

. Then, as

q

is being moved,

Q. The lines of force of the electric field of a positive charge

(+ q)

and a negative charge

(- q)

are shown in figure (a) and (b) below. Then:-

(a) The work done in moving a small positive charge (+

q_{0}

) from Q to P will be positive
(b) The work done in moving a small negative charge (−

q_{0}

) from B to A will be positive
(c) In going from Q to P, the kinetic energy of a small negative charge (−

q_{0}

) increases
(d) In going from B to A, the kinetic energy of a small negative charge (−

q_{0}

) decreases

Work done by electrostatic force to take point charge

Q

from O to O' is. {Where O and O' are center of uniformly charged rings of radius

R

with charge

+ Q

and

Q

. If

\frac{k Q^{2}}{R} = 1

}

Q. A spherical shell with an inner radius 'a' and an outer radius 'b' is made of conducting material. A point charge +Q is placed at the center of the spherical shell and a total charge -q is placed on the shell.
(a) Charge

- q

is distributed on the surfaces as
(A)

- Q

on the inner surface,

- Q

on outer surface
(B)

- Q

on the inner surface,

- q + Q

on outer surface
(C)

+ Q

on the inner surface,

- q - Q

on outer surface
(D) The charge

- q

is spread uniformly between the inner and outer surface.
(b) Assume that the electrostatic potential is zero at an infinite distance from the spherical shell. The electrostatic potential at a distance

R (a < R < b)

from the centre of the shell is

[w h e r e K = \frac{1}{4 π ε_{0}}]

A positive point charge +Q is fixed in space. A negative point charge -q of mass m revolves around a fixed charge in elliptical orbit. The fixed charge +Q is at one focus of the ellipse. The only force acting on negative charge is the electrostatic force due to positive charge. Then which of the following satement is true.

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The correct option is D U decreases If charge is being moved slowly, −→Fa=−−→FE Wa+WE=ΔKE=0 [Charge is moved slowly at constant speed] i.e., Wa=−WE Also WE=−ΔU Thus, Wa=+ΔU As force Fa and displacement are 180∘ →F.→dr<0 Wa<0 Thus, ΔU<0 therefore, U decreases.