1. Consider the Yukawa potential V=g²e r/ro T where r = √√√x² + y² + 2² and is the distance from the origin and ro is a constant. (This potential arises naturally in nuclear physics but we can imagine it being produced by a specific configuration of electric charge) i) Work in a suitable coordinate system and derive the electric field associated with this potential. ii) Compute the flux through a spherical Gaussian surface centred on the origin as a function of r. iii) Use the above result in the limit that r → ∞o to show that the total charge involved is zero.
1. Consider the Yukawa potential V=g²e r/ro T where r = √√√x² + y² + 2² and is the distance from the origin and ro is a constant. (This potential arises naturally in nuclear physics but we can imagine it being produced by a specific configuration of electric charge) i) Work in a suitable coordinate system and derive the electric field associated with this potential. ii) Compute the flux through a spherical Gaussian surface centred on the origin as a function of r. iii) Use the above result in the limit that r → ∞o to show that the total charge involved is zero.
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Transcribed Image Text:1. Consider the Yukawa potential
V = g²e
T/TO
T
where r = √√x² + y² + z² and is the distance from the origin and ro is a constant.
(This potential arises naturally in nuclear physics but we can imagine it being
produced by a specific configuration of electric charge)
i) Work in a suitable coordinate system and derive the electric field associated
with this potential.
ii) Compute the flux through a spherical Gaussian surface centred on the origin
as a function of r.
iii) Use the above result in the limit that r → ∞ to show that the total charge
involved is zero.
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