Question

A length L of wire carries a steady current I. It is bent first to form a circular plane coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same current is ______.

विकल्प

• a quarter of its first value.

• unaltered

• four times of its first value. 

• a half of its first value.

Answer 1

A length L of wire carries a steady current I. It is bent first to form a circular plane coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same current is four times of its first value.

Explanation:

Here n= 2,

B₂ = n² B₁ =2² B=4B

Alternate Method:

The magnetic field at the centre of the current-carrying coil is given by `"B"=µ_0/(4π). (2π"Ni")/r ⇒"B" α N/r`

∴`"B"_1/"B"_2="N"_1/"N"_2xxr_2/r_1`  ....(i)

Given that,

`"N"_1=1,"N"_2=2,r_1=r,r_2=r/2,`

`"B"_1="B"`

∴`"B"/"B"_2=1/2xx(r/2)/r=1/4 ⇒"B"_2=4"B"`  ....[From(i)]