The magnetic field at two points on the axis of a circular coil at distance 0.05m and 0.2m from the centre are in the ratio 8:1.find the radius of the coil?

Asked by rahularun2000 | 19th Jun, 2015, 07:05: PM

Expert Answer:

begin mathsize 14px style straight B equals fraction numerator straight mu subscript 0 Ir squared over denominator 2 left parenthesis straight r squared plus straight x squared right parenthesis to the power of 3 divided by 2 end exponent end fraction Given colon straight B subscript 1 over straight B subscript 2 equals fraction numerator left parenthesis straight r squared plus straight x subscript 2 squared right parenthesis to the power of 3 divided by 2 end exponent over denominator left parenthesis straight r squared plus straight x subscript 1 squared right parenthesis to the power of 3 divided by 2 end exponent end fraction open parentheses 8 over 1 close parentheses squared equals fraction numerator left parenthesis straight r squared plus straight x subscript 2 squared right parenthesis cubed over denominator left parenthesis straight r squared plus straight x subscript 1 squared right parenthesis cubed end fraction 4 left parenthesis straight r squared plus straight x subscript 1 squared right parenthesis equals straight r squared plus straight x subscript 2 squared 4 straight r squared plus 4 straight x subscript 1 squared equals straight r squared plus straight x subscript 2 squared 3 straight r squared equals straight x subscript 2 squared minus 4 straight x subscript 1 squared 3 straight r squared equals left parenthesis 0.2 cross times 0.2 right parenthesis minus 4 left parenthesis 0.05 cross times 0.05 right parenthesis 3 straight r squared equals 0.04 minus 4 left parenthesis 0.0025 right parenthesis 3 straight r squared equals 0.04 minus 0.01 3 straight r squared equals 0.03 straight r squared equals fraction numerator 0.03 over denominator 3 end fraction equals 0.01 straight r equals 0.1 space straight m end style
 
The radius of the coil is 0.1 m.

Answered by Faiza Lambe | 19th Jun, 2015, 08:52: PM