Five long wires A, B, C, D and E, each carrying current I are arranged to form edges of a pentagonal prism as shown in Fig. 4.6. Each carries current out of the plane of paper.


(a) What will be magnetic induction at a point on the axis O? Axis is at a distance R from each wire.


(b) What will be the field if current in one of the wires (say A) is switched off?


(c) What if current in one of the wire (say) A is reversed?



a) The solution to this question is intuitive.


The made at center for pentagon is,


Θ=72°


And the force is always perpendicular to the line joining the wire and the point to be calculated at e.g. OB.


So the force vector is at 90° from OB.


This makes an angle of 18° with OA.


Hence after finding out all the forces we are going to end up in a pentagon (HIJGF) with a shift of 18°.


So, the force at center is 0.


Wires are taken to be infinitely long


b) When we eliminate one wire then;





This is the magnetic induction when one wire is eliminated.


c)



If one wire is revised, then



=


= along FH


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