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Consider an electric circuit such that the whole circuit is entirely within an external uniform magnetic field. This circuit is composed of a current carrying wire in the form of a coil formed of straight parallel wires. The parallel wires in this circuit are all perpendicular to the external magnetic field.

If we want to calculate the magnetic force acting on one of those parallel wires in this coil using $F=IBL \sin \theta$, will $L$ be the whole length of the coil or only one part of it? In other words, will each part of the wire in this circuit (which is perpendicular on the external magnetic field) act as one unit or will each straight line in the coil act separately?

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  • $\begingroup$ Why is this tagged as "biophysics"? Where is the bio part? $\endgroup$
    – nasu
    Mar 7, 2022 at 23:42
  • $\begingroup$ Are you trying to calculate the net force on the whole circuit? That's just zero, the forces on different pieces of wire cancel out. $\endgroup$
    – Puk
    Mar 7, 2022 at 23:56
  • $\begingroup$ this is tagged as biophysics because we are trying to build up a theory that will have an application in the medical field. $\endgroup$ Mar 9, 2022 at 22:19
  • $\begingroup$ No i am not trying to calculate the net force acting on the whole circuit , I am assuming that i have a straight 1 m long wire in a straight uniform magnetic field, then we took the same wire and made it in the form of loops (to occupy less space), those loops of this wire are perpendicular to an external magnetic field, I am trying to calculate the force on one of those loops (part of the 1 m wire) ,Will L be the length of this loop only or will it be the whole length of the wire which is 1 m)... $\endgroup$ Mar 9, 2022 at 22:27

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If you want to calculate the force on only one of the rods, then only the length of that rod is taken into account in $F = IBL$ (since you said, the rods are perpendicular to the external magnetic field, $\sin\theta = 1$).

Hint: If you want to verify why this is true, check how the expression for $F$ is derived in the first place: https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/Book%3A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)/11%3A_Magnetic_Forces_and_Fields/11.05%3A_Magnetic_Force_on_a_Current-Carrying_Conductor

There, they started with a small current element $Idl$ and then integration is performed with limits according to the system in study. Here it is the length of the single rod.

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  • $\begingroup$ So, If i understand you right, if i have a metal instrument (made of ickel-titanium) with length 0.001m stuck inside a tight tube, i will pass a current of 0.001 Amps through this instrument, and a magnetic field of 1 Tesla ,the angle between I and B is 90 so F will be 0.001(m)X0.001(A)X1(T)Xsin90=0.000001N $\endgroup$ Mar 10, 2022 at 4:46
  • $\begingroup$ So, if i want to increase the magnetic force exerted on this instrument ,while I and B are constant, i thought of making this 0.001m long instrument part of an electric circuit of a 10 m long wire ( coiled ) and the whole circuit is within the magnetic field and this magnetic field is perpendicular to the coiled wire, so in this situation if i want to calculate F exerted on this small instrument, Will it remain the same as before or will it increase as the effective L (part of the wire which is perpendicular to the external magnetic field) will increase, F=10(m)X0.001(A)X1(T)Xsin90=0.01N $\endgroup$ Mar 10, 2022 at 4:56
  • $\begingroup$ @TarekHossamAbdelatySarhan Your first comment is correct. The force will be indeed 0.000001 N. $\endgroup$ Mar 13, 2022 at 8:49
  • $\begingroup$ @TarekHossamAbdelatySarhan For your second comment. If I understood you correctly, the "instrument" in both scenarios is 0.001m long and you're interested in the force only on this part of the circuit. If that's the case, the force remains the same in both cases. So in your force equation, you should have l = 0.001 m in both cases. $\endgroup$ Mar 13, 2022 at 8:54
  • $\begingroup$ @TarekHossamAbdelatySarhan Be clear what is your system in study (system = whose force you want to calculate). If your system however is: 0.001 m wire in case-1 and 10 m wire in case-2 (you want to calculate the force on the whole 10 m wire in this case), then l = 10 m and your second comment is correct. So in short, l = length of your system under study (no matter whether it is or it is not a part of a bigger circuit) $\endgroup$ Mar 13, 2022 at 8:58

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