A long straight wire carrying a current of 30 A is placed in an external uniform magnetic field of induction `4xx10^(-4)` T. The magnetic field is acting parallel to the direction of current. The magnitude of the resultant magnetic induction in tesla at a point 2.0 cm away from the wire is `(mu=4pixx10^(-7)Hm^(-1))`

Options

A. `10^(-4)`
B. `3xx10^(-4)`
C. `5xx10^(-4)`
D. `6xx10^(-4)`

Answer

C

Explanation

External uniform magnetic field of induction `B_(1)=4xx10^(-4)J` Magnetic induction at a point the straight conductor carrying current `B_(2)=(mu_(0)i)/(2pir)=(4pixx10^(-7)xx30)/(2xxpixx2xx10^(-2))=3xx10^(-4)J`
Resultant magnetic induction
`B=sqrt(B_(1)^(2)+B_(2)^(2))=sqrt((4xx10^(-4))^(2)+(3xx10^(-4))^(2))=5xx10^(-4)`