Question

Two concentric current loops lie in the same plane. The smaller loop has a radius of 3.6 cm and a current of 12 A. The bigger loop has a current of 20 A . The magnetic field at the center of the loops is found to be zero. What is the radius of the bigger loop?

Answer 1

the radius of bigger loop = 6 cm

Step-by-step explanation:

given,

two concentric current loops

smaller loop radius = 3.6 cm

]current in smaller loop = 12 A

current in the bigger loop = 20 A

magnetic field at the center of loop = 0

Radius of the bigger loop = ?

`B_t = B_1 + B_2`

`0 = (\mu_0I_1)/(2R_1) +(\mu_0I_2)/(2R_2)`

now, on solving

`(I_1)/(R_1) = (I_2)/(R_2)`

`R_2 = I_2(R_1)/(I_1)`

=
`20* (3.6)/(12)`

= 6 cm

hence, the radius of bigger loop = 6 cm