1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Magnetic field components of a circuit

  1. Mar 17, 2016 #1
    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

    \begin{equation}
    \mu = IA
    \end{equation}

    \begin{equation}
    \vec{\tau} = \vec{\mu} X \vec{B}
    \end{equation}

    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:

    \begin{equation}
    \vec{\mu} = -IAk
    \end{equation}

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

    \begin{equation}
    B_x = \frac{3}{IA}
    \end{equation}

    \begin{equation}
    B_y = -\frac{4}{IA}
    \end{equation}

    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. jcsd
  3. Mar 17, 2016 #2
    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.
     
  4. Mar 17, 2016 #3
    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.
     
  5. Mar 17, 2016 #4
    I guess you should include D's in the components otherwise how can you obtain a torque that contains D?
     
  6. Mar 17, 2016 #5
    Alright thanks, must be a typo in the set.
     
  7. Mar 17, 2016 #6
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Magnetic field components of a circuit
Loading...