Two rings X and Y are placed in such a way that their axes are along the X and the Y axes respectively and their centres are at the origin. Both the rings X and Y have the same radii of 3.14 cm. If the current through X and Y rings are 0.6 A and 0.8 A respectively, find the value of the resultant magnetic field at the origin.
`(mu_(0)=4pixx10^(-7)SI)`

Explanation

1. Magnetic field produced in the X-ring due to current `I_(1)=0.6A` is,
`B_(1)=(mu_(0)I_(1))/(2r)" "...(1)`
2. Magnetic field produced in the Y-ring due to current `I_(2)=0.8A` is
`B_(2)=(mu_(0)I_(2))/(2r)" "...(2)`
3. Resultant magnetic field produced near origin is,
`vecB=vecB_(1)+vecB_(2)`
`thereforeB=sqrt(B_(1)^(2)+B_(2)^(2))`
From equation (1) and (2),
`thereforeB=sqrt(((mu_(0)I_(1))/(2r))^(2)+((mu_(0)I_(2))/(2r))^(2))`
= `mu_(0)/(2r)sqrt(I_(1)^(2)+I_(2)^(2))`
= `(4pixx10^(-7))/(2xx3.14xx10^(-2))sqrt((0.6)^(2)+(0.8)^(2))`
= `2xx10^(-5)sqrt(0.36+0.64)`
= `2xx10^(-5)T`
`thereforeB=2xx10^(-5)T`