Force Between Parallel Wires and Magnetic Field of a Wire, Loop and Solenoid Calculator
Find the force between wires and the field of common current arrangements.
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How this calculator works
Choose parallel wires, a straight wire, a loop or a solenoid and enter the currents and dimensions.
For two wires it gives the force for each metre mu0 I1 I2 over 2 pi r, the force on your length and whether they attract (same direction) or repel (opposite).
For the others it gives the field B in millitesla, microtesla or gauss.
Formulas used
- \frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi r}
- B = \frac{\mu_0 I}{2\pi r}
- B = \frac{\mu_0 N I}{2R}
- B = \mu_0 n I
Worked example
With the default numbers in the calculator above:
- Force for each metre of wire: 0.20 mN/m
- Force on the length of wire you gave: 0.0002 N (0.20 mN)
- Direction: The wires attract each other (the currents are in the same direction)
- Field of the first wire at the second wire (the cause of the force): 0.0200 mT
Change the numbers in the calculator to see the full working, every step, for your own case.
A second worked example
A different case, with these numbers: What do you want? Field at the centre of a circular loop.
- Field at the centre of the circular coil: 12.57 mT (125.66 gauss)
Common questions
Do parallel currents attract or repel?
Currents in the same direction attract. Currents in opposite directions repel.
How big is the force?
Small: two wires 1 m apart carrying 1 A each have a force of 2 x 10 to the minus 7 newton per metre, which used to define the ampere.
Does a core change the field?
Yes. A magnetic core multiplies the solenoid field by its relative permeability until it saturates.
Is the field uniform in a solenoid?
Inside a long solenoid it is nearly uniform, and outside it is nearly zero.
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Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any university physics text (Ampere's law and the magnetic force between currents); Griffiths, Introduction to Electrodynamics.
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