A 15-loop circular coil 22 cm in diameter lies in the xy plane. The current in each loop of the coil is 7.6 A clockwise, and an external magnetic field B⃗ =(0.55i^+0.60j^−0.65k^)T passes through the coil.

part A Determine the x, y, and z projections of the magnetic moment of the coil, μ⃗ . Express your answers using two significant figures separated by commas.

part B Determine the x, y, and z projections of the torque on the coil due to the external magnetic field. Express your answers using two significant figures separated by commas. Part C Determine the potential energy U of the coil in the field (take U =0 at θ = π/2). Express your answer to two significant figures and include the appropriate units.

Question

contestada

Respuesta :

lublana lublana · Answer 1 · 2020-04-08T11:41:07+02:00

Answer with Explanation:

We are given that

Number of turns,N=15

Diameter,d=22 cm

Radius,r=[tex]\frac{d}{2}=\frac{22}{2}=11 cm=\frac{11}{100}=0.11 m[/tex]

1 m=100 cm

Current,I=7.6 A

Magnetic field,B=[tex](0.55i+0.6 j-0.65k)T[/tex]

A.Magnetic moment of coil,[tex]\mu=-NIAk=-NI(\pi r^2)k[/tex]

[tex]\mu=-15\times 7.6\times \pi(0.11)^2k=-4.3kAm^2[/tex]

[tex]\mu_x=0,\mu_y=0,\mu_z=-4.3Am^2[/tex]

B.Torque on the coil,[tex]\tau=\mu\times B[/tex]

[tex]\mu\times B=\begin{vmatrix}i&j&k\\0&0)-4.3\\0.55&0.6&-0.65\end{vmatrix}[/tex]

[tex]\mu\times B=2.58i-2.38 j[/tex]

[tex]\tau=2.58i-2.38 j[/tex]

[tex]\tau_x=2.58Nm[/tex]

[tex]\tau_y=-2.38 Nm[/tex]

[tex]\tau_z=0[/tex]

C.Potential energy of coil=[tex]-\mu\cdot B[/tex]

[tex]P.E=-4.3\cdot(0.55i+0.6j-0.65k)=2.8J[/tex]