3 part Electrostatics question.?

Question

Just to get the juices flowing:

1)Discuss the advantages of Helmholtz coils as a provider of uniform field. How much current would it take to provide a region in which the Earth's field was canceled for coils of 1.0-m diameter with 200 turns each?

2) An electron of mass 9.11e-31 kg travels in a circular orbit within a large evacuated chamber. The orbit has a 3.0 mm radius and is perpendicular to a B-field of 0.070 T. What's the electron's speed?

3) A 1.70 m long straight wire experiences a maximum force of 1.90 N when in a uniform 1.340 T B field. What current must be passing through it? [Hint: Maximum force occurs when = 90°.]

Answer 1

1. The strength of the field at the Earth's surface ranges from less than 30 microteslas (0.3 gauss) in an area including most of South America and South Africa to over 60 microteslas (0.6 gauss) around the magnetic poles in northern Canada and south of Australia, and in part of Siberia. (http://en.wikipedia.org/wiki/Earth%27s_magnetic_field#Magnetic_field_electrogenerators)
For Helmholtz coil we can write ( http://en.wikipedia.org/wiki/Helmholtz_coil )

B= [(4/5)^3/2] (u n I/R)
B – magnetic field strength (Tesla)
u= the permeability of free space constant = 4 pi 10 e-7 Tm/A= 1.26 e -6 T m/A
I – current (Amps)
R – coil radius (in meters)
N – number of turns
I=[(5/4)^3/2] B R/(u n)
Since Earth’s magnetic field can varry between 30 and 60 uT it is up to you to chose the value and perform neessary computations.

2. Poorly stated problem. I assume that it travels in the Earth's gravitational field where the magnetic force cancels the gravitational.
F(magnetic)=F(gravitational)
F=q v x B or
F= q |v|| |B| sin (angle between the plan eof motion and mag field) (assuming that the field is at 90 degrees to the plane where the electron moves)
F=q v B
B = u I / (2R) ?(Biot Savart law http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html#c1 )
We have
F=qv u I / (2R)
mg= qv u I / (2R) Be careful about the direction of generated B by an electron and the B acting on it coupled with the gravitational force.
3. Is straight forward (http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magcur.html#c1)
Let me know if it was helpful.