Answer:
a) Bt = 7.73 * 10^-5 T
b) T = 6.94 * 10^-7 N*m
Explanation:
Step 1: Data given
Circumar loop Radius = 13 cm
Current = 16 A
Flat coil radius = 0.63 cm
48 turns
Current = 1.5 A
<em> a) What is the magnitude of (a) the magnetic field produced by the loop at its center</em>
Let's assume a loop concentric with a coil, the plane of the coil is perpendicular to the plane of the loop. The magnetic field due to the loop at the center of the loop can be given by:
Bt = µ0It / 2Rt
In this case we'll get:
Bt = ((4π * 10^-7 T*m/A)(16A)) /(2*0.13m)
<u>Bt = 7.73 * 10^-5 T</u>
<em> b) What is the magnitude of the torque on the coil due to the loop?</em>
The torque magnitude excreting on the coil due to the magnetic field of the loop is given by:
T = µcBtsin(∅)
with µc = the magnetic dipole moment of the coil
with ∅ = the angle between the magnetic dipole moment and the magnetic field. The magnetic dipole moment is given by:
µc = N*Ic*A
⇒ with N = the number of turns in the coil
⇒ with A = πRc² = the area of the coil
µc =π*N*Ic*Rc²
T= π*N*Ic*Rc²*Bt(sin∅)
In this situation we'll have:
T= π*48*1.5A* (0.63 *10^-2m)²*(7.73 * 10^-5 T)*sin(90)
T = <u>6.94 * 10^-7 N*m</u>
