(a) Calculate the magnitude of the magnetic moment of thisloop. | m | = A-m 2 6.

Question

(a) Calculate the magnitude of the magnetic moment of thisloop.

|m| = A-m2   
6.23   NO

HELP:  Use the standard expressionfor the magnitude of the magnetic moment of a current loop (thisexpression applies to a loop of any shape provided it lies in aplane). Keep in mind that for the forces and torques on a currentloop, the relevant current is the net circulating currentN × I where N is the number ofturns and I the current per turn.
HELP:  The area that one uses in themagnetic moment formula is always the area seen in "plan view",i.e., the area seen looking perpendicularly at the loop.

Note: if N is known, but it is not clear from theproblem statement whether the specified current is the netcurrent or the current per turn, you cangenerally assume that the author of the problem means currentper turn. On a quiz or exam, assume nothing and ask forclarification! "Per turns", like "radians", is a quantity that hasno physical dimensions but is very helpful in keeping thingsstraight in calculations.

A spatially uniform magnetic field of strength B = 0.46T points in the +z direction. Let q denote the angle between the plane of theloop and the x-y plane. (See diagram.)

(b) What is the magnitude of the torque on the loop whenq = 0° ?

t = N-m    *
0   OK

(c) What is the magnitude of the torque on the loop whenq = 90° ?

t = N-m    
2.87   NO

HELP:  Use the standard expressionfor the torque on a magnetic moment m in amagnetic field B.
HELP:  For this relative orientation ofthe m and B vectors (the anglebetween them is 90°), what is the magnitude of their crossproduct?

(d) Calculate the components (magnitude and algebraic sign) ofthe torque when q =27°.

tx = N-m   
1.3   NO

ty = N-m    *
0   OK

tz = N-m    *
0   OK

HELP:  First write an expression forn, a unit vector normal (perpendicular) to theplane of the loop, oriented with respect to the current by the RHR(Right Hand Rule). Write it in algebraic form with the angle(27o) denoted by q.
HELP:  Express the magnetic field vectorin terms of unit vectors and then take the cross product to findthe torque. Check your algebraic solution by direct application ofthe RHR for cross products.

A circular loop of radius a = 4.1 cm consists ofN = 20 turns. The current is I = 1.21 A per turn.When viewed looking down the x-axis, the current in thenearest portion of the loop is moving in the direction of the arrowshown in the diagram.

Explanation / Answer

I'm sorry for my last answer. I fixed andsaved it but somehow it didn't work. When i realized, it was toolate bcs it was closed. I'm so sry. Hereis the one i fixed. If it's still wrong,feel free to sms me

(a) Calculate the magnitude of the magnetic moment of thisloop.

|m| = I.N.S = 0.128A-m2    

(b) What is the magnitude of the torque on the loop whenq = 0° ?

t = N-m    *
0   OK

(c) What is the magnitude of the torque on the loop whenq = 90° ?

t = B |m|= 0.059 N-m    

(d) Calculate the components (magnitude and algebraic sign) ofthe torque when q =27°.

tx =B |m| sin q = 0.027N-m

ty = N-m    *
0   OK

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