An infinite solenoid along the z axis in a cylindrical coordinate system has n t
ID: 1311008 • Letter: A
Question
An infinite solenoid along the z axis in a cylindrical coordinate system has n turns per meter and a radius R. Current flows downward through the solenoid at a constant 0 A. A from time t=0 to t=10s then decreases by .1A/s for 10s thens stays at a constant 0A. The solenoid is wound such that downward current flows clockwise as viewed from the +z axis looking down at the origin.
a) On a sketch like the one at left, fill in dots and x's to indicate the current at t=0
b)On the same sketch draw the magnetic field lines at t=0
c)Choose a time when the electric field magnitude is not zero and sketch the electric field lines. Clearly mark which lines are electric and which are magnetic. Make sure to consider the electric field both inside and outside of solenoid.
d)Sketch the electric field magnitude at some fixed position you choose as a funciton of time. This sketch need only be qualitatively correct not quantitatively.
e)Choose a time when the electrid field magnitude is not zero and ifne the electric field magnitude E(r) inside and outside the solenoid.
f)HOw would the answer to part e change if this were a semi infinite solenoid? That is the solenoid extends from z=-inf to z=0 and your are asked to find E(r,z=0). Explain reasoning.
Explanation / Answer
up on assumption
considered for time t=0 t0 t =10 current is constatnt =A ,after t it decress and decress by 1A per second up to next 10 seconds then stays constat at A
for the above assumptions
a)on the +x direction current will inward at the begining ,on the left it's upward means comming out of the plane
if current is 0 Ampers then there won't be any magnetic or electric filed line
b) At t=0 current is constant ,so the magnetic filed also cosnstant
so according to flemming right hand rule wrap your right hand around the loop of solenoid in the direction of flow of current
that give magenetic filed in the +z direction
c) For this consider the time when electirc field decress 1 ampere per second .
as the current through the solenoid changes the induced potential also changes according to this formula
V=-d[Q]/dt where Q=d[B]/di
so V=Ld[i]/dt where L is inducatnce
The polarity (direction) of the induced voltage is given by Lenz's law, which states that it will be such as to oppose the change in current. For example, if the current through an inductor is increasing, the induced voltage will be positive at the terminal through which the current enters and negative at the terminal through which it leaves.
for this case the point where current enters is negetive means electric iled lines terminate at that position
and emarges at positive pole
there will be no electricfiled in side solenoid
==> for magnetic field always use flemming right hand rule thumb gives the magnetic filed direction
if you understna dthis rest you can do
they fallow the same rules
i have given the basic way of approaching the problem