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Electric Charges And Fields

Question

Two circular coils, one of radius r and the other of radius R are placed coaxially with their centres coinciding. For R >> r, obtain an expression for the mutual inductance of the arrangement.

Solution

Given, two circular coils one of radius 'r' and the other of radius 'R' placed coaxially with their centers coinciding.
Suppose a current I₂ flows through the outer circular coil.
Magnetic field at the centre of the coil is

B_{2} = \frac{μ_{0} I_{2}}{2 R}

Magnetic field B₂ may be considered constant over the cross-sectional area of the inner smaller coil.

Hence,

ϕ = B . A .

ϕ_{1} = {πr}^{2} B_{2} = \frac{μ_{0} {πr}^{2} I_{2}}{2 R} = {MI}_{2}

∴

M = \frac{ϕ_{1}}{I_{2}} = \frac{μ_{0} {πr}^{2}}{2 R}

Some More Questions From Electric Charges and Fields Chapter

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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Electric Charges And Fields

Two circular coils, one of radius r and the other of radius R are placed coaxially with their centres coinciding. For R >> r, obtain an expression for the mutual inductance of the arrangement.

Some More Questions From Electric Charges and Fields Chapter

Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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