Question

A circular loop of radius 10 cm carrying current of 1.0 A lies in x-y plane. A long straight wire lies in the same plane parallel to x-axis at a distance of 20 cm as shown in figure.

Find the direction and value of current that has to be maintained in the wire so that the net magnetic field at O is zero.

Answer 1

Magnetic field due to the current carrying loop,

`B_1 = (mu_0I)/(2R)`   ...(at its centre)

⇒ `B_1 = (mu_0 xx 1)/(2 xx 10 xx 10^-2)`   ...(into the plane of the paper)

Magnetic field due to the current carrying wire,

`B_2 = (mu_0I)/(2pir)`

⇒ `B_2 = (mu_0 xx I)/(2pi xx 20 xx 10^-2)T`

Now, according to the question,

B₁ = B₂

So, `mu_0/(2 xx 10 xx 10^-2) = (mu_0I)/(2pi xx 20 xx 10^-2)`

⇒ I = 2π A

⇒ I = 6.28 A

To produce a net magnetic field of zero at 0, the current should flow in the +x direction, and the magnetic field should be directed outward from the paper plane.