A circular coil with 19 -loops has a diameter of 18 cm and lies in the x y plane

Question

A circular coil with   19 -loops has a diameter of   18 cm and lies in the xy plane. Looking down on the coil from a position along the positive z-axis, a current of 8.3 A flows clockwise through the coil. A magnetic field B=(0.55i+0.60j0.65k)T exists in and around the coil.

Part A:

Find the components of the coil's magnetic moment in the x, y, and z directions.Express your answers using two significant figures separated by commas.

     x, y, z = __________________ Am2

Part B

Find the x, y, and z components of the torque on the coil. Express your answers using two significant figures separated by commas.

x, y, z= _________________ mN

Part C

What is the potential energy U of the coil assuming take U = 0 at = /2.

U = __________ ___________

Explanation / Answer

A) magnetic moment = nI.(A vector)

A vetor = cross-section area vector = pi x 0.09^2 k = 0.0254 m^2 k

moment m = 19 x 8.3 x 0.0254 k = 4.01 k

ux = 0

uy = 0

uz = 4.01 A.m^2

B ) torque = m x B

= 4.01 k x ( 0.55i + 0.60j - 0.65k )

= 0.55 x 4.01j - 4.01 x0.60 i

= - 2.405i + 2.205 j N

Tx = -2.405 N Or 2405 mN

Ty = 2.205 N Or 2205 mN

C) U = u.B
  
= (4.01k) ( 0.55i + 0.60j - 0.65k ) = 2.61 J

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