Engineering
Physics
Electric Potential Energy and Electric Potential
Question

In particle and atomic physics, a Yukawa potential (also called a screened Coulomb potential) is a potential of the form VYukawa(r)=-g2e-kmrr, where g is the amplitude of potential, m is the mass of the mediating particle, r is the radial distance to the particle, and k is another constant. The potential is monotonically increasing. this can be realized by appropriate charge distribution. The Coulomb potential of a point charge is an example of a Yukawa potential with e–kmr equal to 1 everywhere. The equation VYukawa(r)=-g2e-kmrr simplifies to the form of the Coulomb potential VCoulomb(r)=-g21r A comparison of the long range potential strength for Yukawa and Coulomb is shown in figure. It can be seen that the Coulomb potential has effect over a greater distance whereas the Yukawa potential approaches zero rather quickly. However, any Yukawa potential or Coulomb potential are non-zero for any large r.

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Linked Question 1

The electric field produced by Yukawa potential is given by

g2e-kmrr(1+kmr)

g2e-kmrr2(1+kmr)

-g2e-kmrr2(1+kmr)

-g2e-kmrr(1+kmr)

Solution
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E=-Vr=g2re-kmrx-km-r2=-g2e-kmrr2[kmr+1].

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Linked Question 2

Yukawa potential becomes coulomb potential at

r → ∞

km → ∞

km → 0

r → 0

Solution
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No Solution.

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Linked Question 3

The correct statement regarding force due to coulomb potential Fc and force due to Yukawa potential Fy.

at small distance, Fy > Fc and at large distances Fc > Fy

at small distance, Fy < Fc and at large distances Fc > Fy

at small distances Fy > Fc and at large distance Fc < Fy

at small distance, Fy < Fc and at large distance Fc < Fy

Solution
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No Solution.

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