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I have one more doubt in the previous question I asked. Doubt: In the figure, what will be the net magnetic field between the wires on the point of intersection. (I think the direction of the magnetic fields due to the two wires won't be opposite on the point of intersection between the wires so, the net magnetic field should not be zero there..)

Asked by arjunsah797 | 25 Jan, 2022, 09:31: AM

Expert Answer

To get answer for this question, we should know , how magnetic field is distributed within the wire of radius R.

Let us consider a long conducting wire of radius R and current I is passing through so that current is distributed uniformly

along the crosssection area of wire.

Current density J = I / ( π R² )

Let us calculate the magnetic field at a radial distance r from central axis of wire so that r < R .

if i is the current passing through crosssection of radius r , then magnetic field at the distance r is given as

begin mathsize 14px style B left parenthesis r right parenthesis space equals space fraction numerator mu subscript o i over denominator 2 pi r end fraction space equals space space fraction numerator mu subscript o over denominator 2 pi r end fraction space cross times space J space cross times pi r squared space equals space space fraction numerator mu subscript o over denominator 2 pi r end fraction space cross times space fraction numerator I over denominator pi R squared end fraction space cross times pi r squared end style

begin mathsize 14px style B left parenthesis r right parenthesis space equals space fraction numerator mu subscript o space I over denominator 2 pi end fraction space cross times space open parentheses r over R squared close parentheses end style

Hence from above expression we see that magnetic field inside the wire directly proportional to radial distance.

Hence at centre i.e., at r = 0 , we have zero magnetic field.

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Hence for the two long current carrying wires that are mutually perpendicular to each other ,

magnetic field is zero at the point of intersection.

Answered by Thiyagarajan K | 25 Jan, 2022, 11:53: AM

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