magnetic field by rotating disc
here's a rotating disc, with surface charge density of sigma. it's hinged to the wall and is being rotated about the hinge. the ans for magnetic field is (mu0omega0sigmaR)/pi using omeganaught for the angular velocity of the disc. Can someone help me with the derivation using integration?
78 Replies
@Gyro Gearloose
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.its hinged on a point on its cicrumference??
Smthing like this ???
pls elaborate on the setup
@ns
yes that's right
i feel like i am near but doing some minor error
i used desmos for the integral and it isnt pi
could we find net magnetic moment and then use 2KM/r^3 to find magnetic field? or do we require the info that we gotta find magnetic field at point at a dist r>>>R??
@hardcoreisdead
i hvnt studied magnetic moment as of now
š do they not teach you that before induction?
magnetic field induction??
(your other doubr)
whin aao
havent done it yet
wait also where did u find the magnetic field @hardcoreisdead
at point O
about the hinge basically
oh
i thought on the axis of the hinge
oh lol it was too easy...u overcomplicated it
@hardcoreisdead
"O" pe nikala hai meine
share soln
@iwishforchristmas @ns
bruh
@hardcoreisdead
element kya hai?
shit i had a class at 4
imagine the disc rotating.....so we would be getting infinite loops from 0 to 2R...x is dist from O (jiske about nikalna hai)
wait i think i made a mistake, i'll check it after 6
ok yes disregard this
very wrong
š
i used bio savart law ( velocity edition) and assumed there were several arcs at a distance 'x' from rotation axis moving with velocity xw and integrated those arcs for a circle
i did smthing similar. can u find the error in mine
how is v and x always perpendicular . the element is in same plane as the disc right??
ye isme element kese liya ha figure smjh ni aarahi
damn nice approach
motion aisa sa hi ha na?
hn
can u explain how did u go from i/A to next line
there should be a dr
the disc is rotatign in x-y plane and radius vecto is always perpendicular to velocity
no liek from i/A to sigma * w/2 pi
i = q/(2pi/W) = sigma area omega/2pi
it doesnt seem so
unless u have a geometrical proof for the same
how is cos theta = x/2R
ohh am mistaken
nah i still dont get perpendicular
circular motion????????
each arc is performing circular motion
@integralofe^2v
hmm by feel i am getting perpendicular
would be great if i get some geometrical proof tho
just take component of R
no basically i have boiled down all of the chrage of the strip to be represented as a point charge at center which is just moving perpendicular to radius vector ( analogus to tangential velocity in circular motion) or u can think of superimposing velocity of ever point on arc ull js end up getting the same ( ill look if can prove it somehow but idts as intuiton is better)
yep this makes sense
your soln is clear to me
did u spot some error in mine?
yes looking at that wait
ty
dont close this please i gotta check this again
the dl element u used in biot savarts law, must be equal to the circumference of the path traced out by that rotating arc, which is 2 * pi * r then u seem to get the correct answer, i can onyl think of 1 explanation as when the arc rotates the current is analogus to as its flowing in a circular wire of radius r (try rotating arc and visualising) then u get the M.F. which is same as M.F. at center of ring, now u consider mulitple such rings traced out by multiple arcs and integrate them all
but still not to sure abt this
thanks so much
dont close rn
didnt get your point
galti kya hai??
yes there shoulnt be theta term here it should be 2pi instead of 2theta as u integrate over entire circular path that arc traces
no?
the db is due to that "element"
yes but that element isnt stationary like basically first u perform integration for 1 element over dl to get 2 pi as u get when u derive the M.F. due to ring liek when u take a small element of section of ring and when u integrate wrt dl of it u get 2 pi right? similiar logic, after perofrming intergation for 1 element u integrate again for all elements
ik its not clear im not able to explain properly
also if i follow this there wont be a pi in my ans
2pi and pi and 4pi ka pi will cut . di ka pi will be cut from xsinx integration
i did it for u here, theres a pi when u bring out current
intergating theta * dr will give u 2R
dr= 2Rsintheta dtheta
now integrate
pi is gone
hold on i integrated wrt r in my solution so i got a cosin inverse term ur integrating wrt theta so let me do by that wait
alrr
i did biot savart with theta and it did match btw
the problem lies in using this result of arc
i just checked integration of -2Rtheta * sin(theta) d theta from limit of pi/2 to 0 is 2R which is same and we already have a pi in denom if u look at my ss
oh shit right
replacing 2theta with 2pi would mean that we are essentially finding field due to a "ring" at centre
which doesnt seem right
if u rotate the arc (element) around what path does it trace?
it does trace a ring
basically this
yaar your point does make sense but i dont understand why
i tried to find the field due a complete ring at its center. i considered an element of dtheta. again i couldnt use the result of field of arc
i had to use u/4pi * 2pi di/R where di = i/2piR * Rdtheta
tbh i never derived the field of ring like this. i always found it at dist x and then put x = 0
right lets firsltyjust see a static rign in which a current is flowing here dl would be entire path integral over the ring right?
en extra R at denom*
which is same as if the ring were rotating, so yea u can compare by tht
okay. when you're done, pls ping
Can u verify my logic
In 2pi/omega time an angle of 2pi is being traversed . i.e the current i derived is travelling 2pi angle in that time so 2theta ki jagah 2pi hoga
Yea the element traverses 2 pi path pretty much yea ig
STILL not 100 percent sure so u shud ask ur teacher
Alr no problem thanx
@ns what was the source
it was a class problem.. (nitin sir insp wale)
@hardcoreisdead can I close this now?
online??
yeah
alr
yeah u can close now
okay
+solved @integralofe^2v @hardcoreisdead @iwishforchristmas
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