Hi, I am having difficulty understanding what to do for these two problems that were on my review package for my exam. I know it involves magnetic fields, solenoids, and bio-savart law but i dont know how to do the problems. Thanks for any help.
A solenoid with 2000 turns is 20-cm long. There is a current if 1.5 A going through the solenoid.
a. Determine the magnitude of the magnetic field in its center.
b. Now, a 2-cm wire carrying a current of 2 A is inserted in the solenoid as shown below. Determine the magnetic force (magnitude and direction) applied on the wire.
2. An AM radio is tuned to a radio station emitting 80 MHz radio waves.
a. What does it mean circuit-wise when the radio is tuned to a station?
b. If the inductor inside the radio is 0.2 μH, what is the capacitance of the variable capacitor?
a. The formula is B = mu_o*I*n
where mu_o, the permeability constant, = 1.26*10^6 henries/m, I = 1.5 A, and n = 2000/0.20 m.
The SI unit for B is the Tesla (which is equivalent to webers/m^2). Plug in the data, your result has units of Tesla.
b. The formula is F = i*l X B. Since the field and the current are at right angles, the magnitude is given by
F = i*l*B
where l is 0.02 m. The Tesla is also equivalent to N/(m.A). Using that form will give you Newtons for the units of your result.
2a. Check these web sites.
Note: the link is supposed to include (radio). I pasted it in, I don't know why it didn't work quite right. You'll have to fix that in your browser.
In the 2nd site, look especially at the section titled Design. It discusses advances over the years. Notice the section titled AM/FM. It says that now the function is accomplished in a chip. You are probably intended to discuss the early method in which the circuit consisted of an inductor and capacitor forming a resonant circuit.
b. Click the link in the 2nd site above (Design section) for resonant circuit. In the responding site, go down to the section Electrical resonance. Click the link for Electrical resonance. Scroll down to LC Circuits. It will show you how the L and C are related to resonant frequency.
I hope this helps,