How are magnetic fields created, what is capacitance energy and voltage

[wosman]

Hello everyone, I hope this is in the right section. if not i'll be happy to move it.

Anyways i have a few questions about general concepts so this may be a lengthy one. Any and all help is REALLY appreciated.

I have attached two photos of something explaining the creation of a magnetic field from an electric field (note: the pictures should show magnetic fields going into the page with an 'x' where the wire is being pulled out and where current eddies are)

So from what I gather is if you change a magnetic or electric field the an electric or magnetic field forms, respectively.

I have no idea how this is happening. It shows a wire being pulled out of a magnetic field i believe and what i THINK happens is the the wire is being removed from the field which means the magnitude of the magnetic field acting on the wire is decreasing (thus changing?) and and this creates an electric field which creates a current (all of this happening magically?) and this current results in the formation of a magnetic field (does this imply anything with a current has a magnetic field?). The magnetic field then forms to 'replace' the loss of field strength from removing the wire from the previous field? Lenz' law seems to say that the new magnetic field will be opposing the inducing field..i don't know why, and certain examples (from the same book) seem to show the opposite where the newly formed magnetic field goes in the same direction as the inducing one.

2. Why is the equation for the energy stored in a capacitor U = 1/2QV. where did the "1/2" come from? certain explanations say "if you were to plot increasing V with increasing Q it would form a positive slope where the area underneath the slope is the energy. this is a triangle shape and thus you must divide the Q x V by 1/2. But this makes no sense to me since it would seem like one could then argue F = ma, thus if you increase a and increase m you will get a slope..and thus F = 1/2 ma, but this isn't true since you take an instantaneous a and m. So if we had a circuit with V = 2 and Q = 2, then why can't we simply say the energy is 2x2? like how grav. potential energy is U = mgh, not 1/2mgh


3. I know that V is the energy per single charge in an electric field depending on it's position 'd' in that field.

but what is V in relation to a circuit? where is the electric field coming from in the circuit? what is 'd' in relation to the field. Why is V change with resistance. I keep hearing fluid/water analogies which do not help.

Again, any help is super appreciated (I have been struggling with these 3 for 2 years (for my MCAT))

 

[cragar]

when they move that loop in a B field the free electrons experience a force called the Lorentz force F=q(vxB) and when one electron moves it pushes the one in front of it because of their E field, so a current starts to flow around the loop. In classical E&M magnetic fields are produced by currents. the 1/2 comes from integration dw= \frac{qdq}{c}
w= \frac{q^2}{2c}
q=cV
suppose I am looking at a parallel plate capacitor at rest, I would see an E field . But now suppose I am moving by it at a speed v and I am moving perpendicular to the E field, I would see a Magnetic field because now I have a current a flow of electrons. Thats one way to get a B field from an E field.