A long solenoid with its axis as the z-axis and uniform cross-section perpendicular to the z-axis carries a current I and has a turn density n in vacuum.
Compute the magnetic field it produces everywhere if its cross-section is circular.
WHAT IS THE FINAL ANSWER TO THE MECHANICS QUESTION?????????????????????????????????????????????????????????????????????????????????????
ReplyDeletehi!
ReplyDeletesome people have elaborated the solution of that question, and there are many answers present. if you disagree, challenge them on that thread.
bhaiya if the solenoid is long enough
ReplyDeletethen by using amperes law
b inside the solenoid id Uoni
and
b outsibe the solenoid is 0
somebody please answer:
ReplyDeletehttp://pratikjain2000.blogspot.com/2011/08/relativity-problem.html
http://pratikjain2000.blogspot.com/2011/08/anybody-there-who-can-show-maximum.html
yes,getting same as rishabh.
ReplyDelete@abhishek-i think mayank has got the right answer
ReplyDeletesame result is applicable for all four question
ReplyDeleteby the amperes law
those who completed it.. tried the next one??
ReplyDeleteThis comment has been removed by a blog administrator.
ReplyDelete@Mayank: that's only when u know its still straight!
ReplyDeleteor can u use ampere's law without even knowing the direction of the field??
No,we can't use it until we know the direction of the field.However, in the given question, it is sufficient to know that the field lines will be in a plane perpendicular to the CS Area vector.
ReplyDeleteP.S.: Is the same formula valid if the cross section is not uniform?
"However, in the given question, it is sufficient to know that the field lines will be in a plane perpendicular to the CS Area vector." ... u mean parallel? and how? u can't just get away saying things are like the way u say!
ReplyDeleteSorry, i meant parallel to the CSA vector.Considering a rectangular amperian curve, one of the sides inside the solenoid parallel to the axis of the solenoid and the other(parallel) one outside, all the pts. on the side inside will have same component of B in the direction of axis (symmetry)--> Valid for an infinite solenoid with any CS.For the possibility of field lines along any other axes we can consider an Amperian loop in the shape of a circle, whose plane is perpendicular to the axis of the solenoid and is centered on the axis of symmetry of the solenoid.From symmetry, we can say that if the magnetic field has a component parallel to the dl vectors on the curve, then it must be same for every dl vector on the closed path which comes out to be zero from the ampere's law. Therefore, we can say that field lines will be parallel to the axis of the solenoid.Similarly, true for an infinite solenoid for any regular CS.For a solenoid(infinite) with any random CS all the other components will cancel out(due to symmetry about any plane perpendicular to the area vector).
ReplyDelete(Not sure about the last statement)
at least according to my visualization of symmetry.. u need guts to establish such a strong conclusion..
ReplyDeletei seriously doubt some of your conclusions here..
ReplyDeleteBhaiya, plz. correct me if i am wrong with the conclusions anywhere (especially the last one).
ReplyDeleteIf possible, plz. post the solution to the last one (long solenoid with any random CS).I thought a lot over it and that(my previous post) was all I got.
This comment has been removed by a blog administrator.
ReplyDelete@Mayank: see, u say ... "From symmetry, we can say that if the magnetic field has a component parallel to the dl vectors on the curve, then it must be same for every dl vector on the closed path".. firstly.. what about the radial component??
ReplyDeleteand then.. I am at a total failure as to understand how u extended the concept to "random shapes"!
For the random shapes, i used the symmetry about any plane perpendicular to the area vector leaving out only the parallel components and cancelling out all others.(same as what has been done in the solution)
ReplyDeleteFor the radial component, again the same symmetry(about any plane perpendicular to the area vector) is applicable.
Else, assuming the radial components to be radially inward, if seen from one side, and then if we flip the solenoid about any axis perpendicular to the area vector, radial field will seem to be exactly the same (inwards again) while this has to be opposite the previous as flipping the solenoid will be equivalent to reversing the direction of current.Hence it should be zero.
(I know this is a kind of reasoning which should not be used to answer such questions, but i would like to know if it's correct and can be applied to some other problems too)
consider a single square element.inside it,the field lines coming out of the plane of square will be parallel to the area vector.the lines will be parallel for a short distance,say dl.now if we put another square element on top of this,dl will become 2dl.this way if lenght of the solenoid is l,field lines will be parallel for a lenght l (or l-dl atleast,considering they become curved at the top).since solenoid is long,l will tend to infinity and field lines can be considered parallel to area vector.after that question will be solved by considering a rectangular amperian surface (like we for long solenoid will circular cross section)
ReplyDeletenot sure,plz tell if its's correct