Question

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.

Answer 1

Answer with Explanation:

We are given that

Number of turns,N=15

Diameter,d=22 cm

Radius,r=
`(d)/(2)=(22)/(2)=11 cm=(11)/(100)=0.11 m`

1 m=100 cm

Current,I=7.6 A

Magnetic field,B=
`(0.55i+0.6 j-0.65k)T`

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

`\mu=-15* 7.6* \pi(0.11)^2k=-4.3kAm^2`

`\mu_x=0,\mu_y=0,\mu_z=-4.3Am^2`

B.Torque on the coil,
`\tau=\mu* B`

`\mu* B=\begin{vmatrix}i&j&k\\0&0)-4.3\\0.55&0.6&-0.65\end{vmatrix}`

`\mu* B=2.58i-2.38 j`

`\tau=2.58i-2.38 j`

`\tau_x=2.58Nm`

`\tau_y=-2.38 Nm`

`\tau_z=0`

C.Potential energy of coil=
`-\mu\cdot B`

`P.E=-4.3\cdot(0.55i+0.6j-0.65k)=2.8J`