Question

Derive an expression for the potential at a point due to a magnetic shell

Answer 1

Answer:

Explanation:

- Integrating this expression with respect to s, so as to take into account all the .... or, the potential due to a magnetic shell at any point is the product of its ..... We may calculate the solid angle ω directly from the definition thus.

Answer 2

The potential at a point due to a magnetic shell V = μ₀/4π Φω

• Take a uniform magnetic shell of strength Φ. Let P is point in shell and O is the center of the shell, the distance between P to O is R. Draw OP which makes an angle θ with the normal of the shell.

Now we will find the potential at any point.

• Consider dA as a small element of area of the shell around O.

⇒ The magnetic moment of the element in the shell m = Φ dA,

⇒ Magnetic moment of the element along OP = Φ dA cos θ

• Therefore, Potential at P due to the element of area dA is

dV = μ₀/4π ΦdA cos θ/R²

• As we know dA cos θ/R² = dω, [the solid angle subtended by the element at point P]

⇒ dV = μ₀/4π Φ dω

• The potential due to the shell is the sum of the potential due to all such elements.

• Therefore, the total potential at P due to the entire shell is given by

V = μ₀/4π ∫ Φ dω

Sine the magnetic shell uniform shell in Φ will be same at all points.

⇒V = μ₀/4π Φ ∫dω

• Which can we written as V = μ₀/4π Φω (In Vacuum). Where ω is the solid angle subtended at P by the entire shell.

Thus, we can conclude the magnetic potential at a point due to a uniform magnetic shell is μ₀/4π times the strength of the shell  

The potential at a point due to a magnetic shell V = μ₀/4π Φω

  #SPJ2