Question

A coil of radius 'r' is placed on another coil (whose radius is 'R' and current flowing through it is changing) so that their centres coincide. (R>>r) if both the coils are coplanar then the mutual inductance between them is proportional to ______.

Options

• `"R"/"r"^2`

• `"r"^2/"R"`

• `"R"/"r"`

• `"r"/"R"`

Answer 1

A coil of radius 'r' is placed on another coil (whose radius is 'R' and current flowing through it is changing) so that their centres coincide. (R>>r) if both the coils are coplanar then the mutual inductance between them is proportional to `underline("r"^2/"R")`.

Explanation:

Magnetic field at the centre B = `(mu_0"I")/"R"`

Φ = Magnetic flux passing through the smaller coil = πr²B

`therefore phi = pi"r"^2 xx (mu_0"I")/"R"`

`therefore "M" = phi/"I" = (mupi"r"^2)/"R"`

`therefore "M" prop "r"^2/"R"`