Home > CSIR NET > A set N concentric circular loops of wire, each carrying a steady current I in the same direction, is arranged in a plane. The radius of the first loop is`r_1` = a and the radius of the `n^(th)` loop is given by `r_n=nr_(n-1)`.The magnitude B of the magnetic field at the centre of the circles in the limit N→∞, is [NET JUNE 2017]

A set N concentric circular loops of wire, each carrying a steady current I in the same direction, is arranged in a plane. The radius of the first loop is`r_1` = a and the radius of the `n^(th)` loop is given by `r_n=nr_(n-1)`.The magnitude B of the magnetic field at the centre of the circles in the limit N→∞, is [NET JUNE 2017]

A set N concentric circular loops of wire, each carrying a steady current I in the same direction, is arranged in a plane. The radius of the first loo

Physics INK

Problem: A set N concentric circular loops of wire, each carrying a steady current I in the same direction, is arranged in a plane. The radius of the first loop is`r_1` = a and the radius of the `n^(th)` loop is given by `r_n=nr_(n-1)`.The magnitude B of the magnetic field at the centre of the circles in the limit N→∞, is [NET JUNE 2017]

(A) `(mu_0I(e^2-1))/(4pia)` (B) `(mu_0I(e-1))/(pia)` (C) `(mu_0I(e^2-1))/(8a)` ✅(D) `(mu_0I(e-1))/(2a)`

Answer:

Given `r_n=nr_(n-1)` and `r_1=a`

The magnetic field at the center of the `n^(th)` circle is

`B_n=(mu_0I)/(2r_n)`

The magnetic field due to all rings is

`B=sum_(n=1)^oo(mu_0I)/(2r_n)`

or, `B=(mu_0I)/(2)[1/r_1+1/r_2+1/r_3+...]`

or, `B=(mu_0I)/(2)[1/a+1/(2a)+1/(3xx2a)...]`

or, `B=(mu_0I)/(2a)[1/(1!)+1/(2!)+1/(3!)...]`

or, `B=(mu_0I)/(2a)[1+1/(1!)+1/(2!)+1/(3!)...-1]`

or, `B=(mu_0I)/(2a)(e-1)`