Question

1. Consider a circular surface of radius a, carrying a uniform surface charge density ?. The circle is in the z = 0 plane with its centre at the origin. A point particle of charge q initially at the centre of the circle is moved to infinity without changing its kinetic energy; that is, it is moved very slowly from its initial position, all the way to infinity. (a) Assuming that the charge is moved purely radially from the origin, derive an expression for the work needed to perform this operation. Here, the charge is moved in the x - y plane, and its z coordinate remains zero at all times. (b) Compare your answer to the work needed to carry the charge to infinity if, this time, it is moved along the z axis; that is, it is moved perpendicularly to the plane of the circle. (c) In this second scenario, derive an expression for the force needed to pull the charge away from the circular surface, as it just leaves the surface. That is, the charge is no longer in the surface, but infinitesimally close to it.

          1. Consider a circular surface of radius a, carrying a uniform surface charge density ?.
The circle is in the z = 0 plane with its centre at the origin. A point particle of charge
q initially at the centre of the circle is moved to infinity without changing its kinetic
energy; that is, it is moved very slowly from its initial position, all the way to infinity.
(a) Assuming that the charge is moved purely radially from the origin, derive an
expression for the work needed to perform this operation. Here, the charge is
moved in the x - y plane, and its z coordinate remains zero at all times.
(b) Compare your answer to the work needed to carry the charge to infinity if, this
time, it is moved along the z axis; that is, it is moved perpendicularly to the plane
of the circle.
(c) In this second scenario, derive an expression for the force needed to pull the charge
away from the circular surface, as it just leaves the surface. That is, the charge
is no longer in the surface, but infinitesimally close to it.

1. Consider a circular surface of radius a, carrying a uniform surface charge density ?.
The circle is in the z = 0 plane with its centre at the origin. A point particle of charge
q initially at the centre of the circle is moved to infinity without changing its kinetic
energy; that is, it is moved very slowly from its initial position, all the way to infinity.
(a) Assuming that the charge is moved purely radially from the origin, derive an
expression for the work needed to perform this operation. Here, the charge is
moved in the x - y plane, and its z coordinate remains zero at all times.
(b) Compare your answer to the work needed to carry the charge to infinity if, this
time, it is moved along the z axis; that is, it is moved perpendicularly to the plane
of the circle.
(c) In this second scenario, derive an expression for the force needed to pull the charge
away from the circular surface, as it just leaves the surface. That is, the charge
is no longer in the surface, but infinitesimally close to it.

Added by Zachary H.

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