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1. Homework Statement
You are a member of a research team studying magnetotactic bacteria. Magnetotactic
bacteria from the southern hemisphere preferentially swim to the south along magnetic
field lines, while similar bacteria from the northern hemisphere preferentially swim to
the north along magnetic field lines. Your team wishes to quantify the behavior o f
magnetotactic bacteria in closely controlled magnetic fields.
You know from your physics class that a coil of wire can be used to produce a magnetic
field, which can be varied by changing the current through it. You set yourself the task
of calculating the magnetic field along the axis of the coil as a function of its current,
number of turns, radius, and the distance along the axis from the center of the coil. To
make sure you are correct, you decide to compare your calculation to measurements.
Calculate the magnitude of the magnetic field as a function of the position along the
central axis of a coil of known radius, the number of turns of wire, and the electric
current in the coil.
2. Homework Equations
BielSavart Law: B = µ0/4π ∫c Idl x r / r3
3. The Attempt at a Solution
I was going to see if someone would be able to check to see if I did the derivation correctly? Thanks so much!
See attached document for diagram of situation.
Derived equation:
∫ dBz = ∫ µ_{0} N I dl cos θ/4π (R^{2} + z^{2}) (R/√R^{2} + z^{2})
µ_{0} N I R / 4π (R2 + z2)3/2 ∫ dl
2π µ_{0} I N R^{2} / 4π (R^{2} + z^{2})^{3/2}
µ_{0} I N R^{2} / 2 (R^{2} + z^{2})^{3/2}final equation.
You are a member of a research team studying magnetotactic bacteria. Magnetotactic
bacteria from the southern hemisphere preferentially swim to the south along magnetic
field lines, while similar bacteria from the northern hemisphere preferentially swim to
the north along magnetic field lines. Your team wishes to quantify the behavior o f
magnetotactic bacteria in closely controlled magnetic fields.
You know from your physics class that a coil of wire can be used to produce a magnetic
field, which can be varied by changing the current through it. You set yourself the task
of calculating the magnetic field along the axis of the coil as a function of its current,
number of turns, radius, and the distance along the axis from the center of the coil. To
make sure you are correct, you decide to compare your calculation to measurements.
Calculate the magnitude of the magnetic field as a function of the position along the
central axis of a coil of known radius, the number of turns of wire, and the electric
current in the coil.
2. Homework Equations
BielSavart Law: B = µ0/4π ∫c Idl x r / r3
3. The Attempt at a Solution
I was going to see if someone would be able to check to see if I did the derivation correctly? Thanks so much!
See attached document for diagram of situation.
Derived equation:
∫ dBz = ∫ µ_{0} N I dl cos θ/4π (R^{2} + z^{2}) (R/√R^{2} + z^{2})
µ_{0} N I R / 4π (R2 + z2)3/2 ∫ dl
2π µ_{0} I N R^{2} / 4π (R^{2} + z^{2})^{3/2}
µ_{0} I N R^{2} / 2 (R^{2} + z^{2})^{3/2}final equation.
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