Question

A circular loop of radius 11.9 cm is placed in a uniform magnetic field.

(a) If the field is directed perpendicular to the plane of the loop and the magnetic flux through the loop is 7.40 ✕ 10⁻³ T · m², what is the strength of the magnetic field?
T

(b) If the magnetic field is directed parallel to the plane of the loop, what is the magnetic flux through the loop?
T · m²

Answer 1

Here it is given that magnetic field is directed perpendicularly to the plane , so flux will be maximum, Since the angle between normal to the loop and magnetic field θ=0

MAGNETIC FLUX,
Φ =BACos θ
Here θ=0 . Therefore

MAGNETIC FLUX,
Φ = BA, where B= magnetic field, A=area

Now we have given value of flux

Φ =7.40×10^-3Tm2

Now we have radius r=11.9cm=0.119m

Therefore area A=πr²=π×(0.119)²=0.04446m²

Cos0°=1

Substituting all the values

Φ =BACos0°

7.40×10^-3=B×0.04446

B=7.40×10^-3/0.04446

B=0.16644=166.44×10³T

b) since magnetic field is parallel to the plane therefore the value of θ=90° which causes the flux to be minimum as zero since cos90=0

Therefore, flux through the loop is zero