IIT JEE , AIEEE Forum - Physics , Magnetism

vpy

Find the magnitude and direction of the magnetic induction of vector B

a) of an infinte plane carrying a current of linear density i, the vector i is same at all points of the plane

b) of two parallel infinte planes carrying a current of linear density i and -i, both the vectors being the same at all points of the plane

This question will be done thru ampere's law, but how to make the amperean loop???

krishna.gopal

Hi vpy, symetry suggests that at any point there will be no component of field perpendicular to plane or along the direction of current. So the field will be parallel to plane but perpendicular to direction of current. Suppose i want to find field at a distance x from the plane. Make a rectangular loop of sides l and 2x such that plane cuts the 2x sides in between. Now_{[ ]}

^{[ ]} B.dl on 2x sides will be zer (Field and path are perpendicular). So _{[ ]}

^{[ ]} B.dl=B*2l=2Bl (as direction of field on two sides will be opposite)
2Bl=

_oil
So B =

_oi/2.

This will be independent of distance from the plane.

(b) If current density is i and -i. The field will be vector sum of two fields. For oints in between the planes the two fields add up and hence field is

_oi. For other points they cancel each other and hence field is zero

mohit1

i am not able to understand the direction of the field. please make me clear

krishna.gopal

Suppose you want o find field at a point P which is at a distance d from plane. Drop a perpendicular PO from P on the plane. At O make an axis (say x-axis) perpendicular to direction of current. Now take a thin strip of current carrying conductor lying between x and x+dx. It carries a current of idx. For every such strip there will be another strip llying between -x and -(x+dx) which will also be carrying equall current. Now if you want to find resultant of these to field, you will find that component perpendicular to plane will be cancelled while that along x will add up. So Net field will be along x-axis.

This is true for a strip at any x. So taking all strips from 0 to

. We find that net field at P is parallel to x-axis

bhupesh

Dear

What you can do is draw a rectangular or square amperian loop such that that two sides each of length say" l " parallel to the sheet and rest two sides will obviously become perpendicular to the sheet isn't it then by symetry and from amperes law

2Bl =

₀ jl

so B= (

₀ ji)/ 2l

I believe for your second question you can find the resultant of two B s

Lois

@ krishna.gopal
for (b)
How do the fields cancel out for other points? I think the field between the plates is

_oi and on the other side of both the plates it is

_oi/2. Correct me if I'm wrong.

bhupesh

Dear
You can use right hand curl rule to see why the field is zero except between the plates like in case of two wires .

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