A long wire carries a current of `20A` along the directed axis of a long solenoid. The field due to a solenoid is `4mT`. Find the resultant field at a point `3mm` from the solenoid axis.

Options

A. 1.33 mT
B. 4.2 mT
C. 2.1 mT
D. 8.4 mT

Answer

B

Explanation

`B_(wire) = (mu_(0))/(4pi) xx(2l)/(r) = (10^(-7) xx 2 xx 30)/(3xx10^(-3))`
` = (4)/(3) xx 10^(-3) T = (4)/(3)mT`
Field due to solenoid
`B_("solenoid") = 4mT`
Resultant magnetic field
`=sqrt((B_(wire))^(2) + (B_("solenoid"))^(2))`
` = sqrt(((4)/(3))^(2) + (4)^(2)) = 4.2mT`