A coil carrying a current experiences a torque when placed in a magnetic field. This torque is quantified by the following relation:
τ=N⋅I⋅A⋅B⋅sin‌θwhere
N is the number of turns in the coil,
I is the current flowing through the coil,
A is the area of the coil,
B is the magnetic field strength, and
θ is the angle between the magnetic field and the normal to the plane of the coil.
The torque is at its maximum when
sin‌θ=1, which occurs at
θ=90∘. Thus, the maximum torque
Ï„max can be expressed as:
Ï„max=Nâ‹…Iâ‹…Aâ‹…BAccording to the problem, the experienced torque is
80% of this maximum:
N⋅I⋅A⋅B⋅sin‌θ=0.8⋅τmaxSubstituting
τ‌max ‌ from equation (i):
N⋅I⋅A⋅B⋅sin‌θ=‌⋅(N⋅I⋅A⋅B)This simplifies to:
sin‌θ=‌We know that:
cos‌θ=√1−sin‌2θ=‌Thus, the tangent of the angle
θ becomes:
tan‌θ=‌=‌=‌Therefore, the angle
θ is:
θ=tan−1(‌)