What is the answer?

Asked by sanabamdiana46 | 13th Nov, 2020, 06:33: PM

Expert Answer:

Let us assume current I is passing through a wire of hollow cylindrical crosssection with inner radius Ri and outer radius Ro .
 
By Ampere's law , magnetic field induction B(r) at a radial distance from center of cross section is given as ,
 
begin mathsize 14px style B left parenthesis r right parenthesis space equals space fraction numerator mu subscript o over denominator 2 pi r end fraction I subscript e n c end subscript end style
where Ienc is enclosed current with in the circle of radius r drawn with centre as centre of crossection of hollow cylinderical wire .
 
At a distance r ≤ Ri , enclosed current is zero . Hence Magnetic field is zero
 
At a distance r such that   Ri ≤ r ≤ Ro , enclosed current  I enc= current density × crosssection area 
 
begin mathsize 14px style I subscript e n c subscript space end subscript equals space fraction numerator I over denominator pi open parentheses R subscript o superscript 2 space minus space R subscript i superscript 2 close parentheses end fraction cross times pi left parenthesis space r squared space minus space R subscript i superscript 2 right parenthesis space equals space I space cross times fraction numerator left parenthesis space r squared space minus space R subscript i superscript 2 right parenthesis space over denominator open parentheses R subscript o superscript 2 space minus space R subscript i superscript 2 close parentheses end fraction end style
 
Magnetic field B at a distance r such that   Ri ≤ r ≤ Ro , 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 cross times fraction numerator open parentheses r squared space minus space R subscript i superscript 2 close parentheses over denominator open parentheses R subscript o superscript 2 space minus space R subscript i superscript 2 close parentheses end fraction end style
At a distance r such that   r > Ro , enclosed current  I enc is the total current passing through wire.
 
Hence magnetic field ar r > Ro 
 
begin mathsize 14px style B left parenthesis r right parenthesis space equals space fraction numerator mu subscript o over denominator 2 pi r end fraction I end style

Answered by Thiyagarajan K | 14th Nov, 2020, 11:38: AM

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