A long vertical wire carriers a current of `10` amperes flowing upwards through it at place where the horizontal component of the earth's magnetic induction is `0.3` gauss. Then the total magnetic induction at a point `5 cm` from the wire due magnetic north of the wire is

Options

A. `0.7` gauss
B. `0.5` gauss
C. `0.1` gauss
D. `0.4` gauss

Answer

B

Explanation

The magnetic induction `B` due to a current `I` ampere a long straight conductor at a distance `r` meter from is given by:
`B=(mu_(0)I)/(4pi)xx((2I)/r)`
Here `I=10amp,r=5cm=5xx10^(-2)m`
`B=10^(-7)xx((2xx10)/(5xx10^(-2)))=0.4` gauss
Since this point is due magnetic north of conductor, the line of action of `vecB` is along earth west direction. Magnetic induction due to earth horizontal component is `0.3` gauss in a direction from south to north.
Resultant magnetic induction `Br` is given by:
`B_(r)=sqrt((0.4)^(2)+(0.3)^(2))=0.5 gauss`