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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) |
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Answer» Solution :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` |
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