Question

A circular area with a radius of 6.20 cm lies in the xy-plane.

Part A) What is the magnitude of the magnetic flux through this circle due to a uniform magnetic field with a magnitude of 0.220 T in the + z -direction?

Part B) What is the magnitude of the magnetic flux through this circle due to the same magnetic field (with a magnitude of 0.220 T ), now at an angle of 54.4 ∘ from the + z -direction?

Part C) What is the magnitude of the magnetic flux through this circle due to the same magnetic field (with a magntiude of 0.220 T ), now in the + y -direction?

Answer 1

here,

the radius of the cirular area , r = 6.2 cm = 0.062 m

A)

magnetic feild , B = 0.22 T

the magnitude of the magnetic flux through this circle due to a uniform magnetic field , phi1 = B * A * cos(0)

phi1 = 0.22 * (pi * 0.062^2) Wb

phi1 = 2.66 * 10^-3 Wb

B)

theta = 54.4 degree

the magnitude of the magnetic flux through this circle due to a uniform magnetic field , phi2 = B * A * cos(54.4)

phi2 = 0.22 * (pi * 0.062^2) * cos(54.4) Wb

phi2 = 1.55 * 10^-3 Wb

C)

theta = 90 degree

the magnitude of the magnetic flux through this circle due to a uniform magnetic field , phi3 = B * A * cos(90)

phi3 = 0.22 * (pi * 0.062^2) * cos(90) Wb

phi3 = 0 Wb