Answer:
Radius of bigger loop(R) =4.5cm
Explanation:
Consider a circular path of radius r around the wire. The magnetic field along that path is given by ;
∫B*dl = k*I where I is the current enclosed. From symmetry, ∫B*dl = 2*π*r*B
B = K*I/r, so the magnetic field varies inversely as the loop radius and directly as the current.
The smaller loop current to radius ratio is 12/2.7
The bigger loop current to radius ratio is = 20/R
12/2.7 = 20/R
R = (20 * 2.7)/12
R=54/12
R=4.5cm
Answer:
Explanation:
The B-field at the center of a circular loop of radius, r and current, I is;
Magnetic field, B = (μ × I) ÷ 2pi × R
Given:
rs = 2.7 cm
= 0.027 m
Is = 12 A
Ib = 20 A
(μ × Is)/2 × rs = (μ × Ib)/2 × rb
Inputting values,
rb = (20 × 2 × 0.027)/12 × 2
= 0.045 m
= 4.5 cm.
