Question

A circular coil of radius R is carrying a current l₁ in anti-clockwise sense. A long straight wire is carrying current l₂ in the negative direction of X-axis. Both are placed in the same plane and the distance between center of coil and straight wire is d. The magnetic field at the centre of coil will be zero for the value of d equal to

Options

• `"R"/pi(l_2/l_1)`

• `pi/"R"(l_2/l_1)`

• `pi/"R"(l_1/l_2)`

• `"R"/pi(l_1/l_2)`

Answer 1

`"R"/pi(l_2/l_1)`

Explanation:

Consider the figure shown below,

The magnetic field due to the circular coil at its centre is given by

`"B"_1 = (mu_0l_1)/(2"R")`(outward)

The magnetic field due to the wire at O is given by

`"B"_2 = (mu_0l_2)/(2pi"d")`

The net magnetic field at the centre of coil is zero.

∴ `"B"_1 - "B"_2 = 0`

`"B"_1 = (mu_0l_1)/(2"R") - (mu_0l_2)/(2pi"d") = 0`

d = `(l_2/l_1)"R"/pi`