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There exist magnetic field vec(B)=yhat(i...

There exist magnetic field `vec(B)=yhat(i)-xhat(j)` in space. What is current (in amperes) crossing through the area enclosed by a circle `x^(2)+y^(2)=a^(2),z=0`. Here radius of circle `a=1`mm

Text Solution

Verified by Experts

The correct Answer is:
5

Magnitude of magnetic field on circle `=B=sqrt(y^(2)+x^(2))=` constant
`ointvecB.dvecl=B 2pia=2pia^(2)`
`4pixx10^(-7)xxI_("in")=2pia^(2)`
`I_("in")=(a^(2))/(2xx10^(-7))=(1xx10^(-6))/(2xx10^(-7))=5A`
Alternate
`B=(mu_(0)I)/(2pir)`
`sqrt(y^(2)+x^(2))=(mu_(0)I)/(2pi sqrt(y^(2)+x^(2)))`
`impliesa^(2)=(mu_(0)I)/(2pi)impliesI=(a^(2))/(2xx10^(-7))=5A`
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