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pitbull
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Homework Statement
You have a spring of length l, radius R, with N loops and n loops per unit length. If you consider it a solenoid, what current do you need to apply to withstand a mass m hanging from it, without stretching or shrinking the spring.
Homework Equations
Magnetic field inside a solenoid: B=μ0nIz
Magnetic energy: W=∫∫∫B2/(2μ0)dV
The Attempt at a Solution
I calculated the magnetic energy of a solenoid and I got:
W=μ0N2I2πR2/(2l)
The force applied by the mass is:
F=mg
So, the magnetic force that I need is:
F=∇W(length constant)=μ0N2IπR2/(l)
Both forces must be equal. I solve for I and I get:
I=mgl/(μ0N2πR2)
Do you thing it is right?
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