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

Answer:

the radius of bigger loop = 6 cm

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 = ?

$B_t = B_1 + B_2$

$0 = \dfrac{\mu_0I_1}{2R_1} +\dfrac{\mu_0I_2}{2R_2}$

now, on solving

$\dfrac{I_1}{R_1} = \dfrac{I_2}{R_2}$

$R_2 = I_2\dfrac{R_1}{I_1}$

       = $20\times \dfrac{3.6}{12}$

       = 6 cm

hence, the radius of bigger loop = 6 cm