# Homework Help: Magnetic field components of a circuit

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1. Mar 17, 2016

### Erik P

1. The problem statement, all variables and given/known data
A circle-formed circuit with an area A lies in the (xy)-plane. An electric current I runs clockwise through the circuit (figure 1). An external magnetic field B exerts a torque t = D(3i - 4j) on the circuit, where D is a positive constant, i is the x-axis unit vector and j is the y-axis unit vector.

a.) Determine the circuits magnetic moment u and determine the magnetic field's components Bx and By.

2. Relevant equations
Right hand rule

\mu = IA

\vec{\tau} = \vec{\mu} X \vec{B}

3. The attempt at a solution
Solved the first part using the right hand rule, the magnetic moment is in the -z axis so we get:

\vec{\mu} = -IAk

For the second part I know what it is supposed to be, but I get something different.

B_x = \frac{3}{IA}

B_y = -\frac{4}{IA}

But those answers are incorrect, the real answers have the 4 and 3 traded around and both are positive, instead of By being negative. Anyone able to tell me why that is? I figure that since 3 is multiplied by the x-axis unit vector that it should then be a part of Bx not By.

2. Mar 17, 2016

### Guneykan Ozgul

Make sure that you are doing the cross product correctly. The other equations seems correct. It seems the mistake is in the cross product. When you cross i×k you should get -j and when you cross j×k you should get i.

3. Mar 17, 2016

### Erik P

Redid the math, sure enough I made a mistake. Quick question though, should D not be included in the components? The answer says not, but I'm not sure on the reasoning.

4. Mar 17, 2016

### Guneykan Ozgul

I guess you should include D's in the components otherwise how can you obtain a torque that contains D?

5. Mar 17, 2016

### Erik P

Alright thanks, must be a typo in the set.

6. Mar 17, 2016

### Erik P

Are you by any chance familiar with conversion of electrical energy to heat in coils/solenoids? Can't seem to figure out how to solve a problem involving that. Basically I need to calculate the total energy converted to heat in a solenoid for t>=, it's the last part of a 3 part problem, already solved the other 2 parts. I can't seem to find anything in my book or online about heat generation of coils. Could use an equation/law that describes it or something that I can convert into an expression that describes it.