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A rigid circular loop of radius r & mass...

A rigid circular loop of radius r & mass m lies in the xy plane on a flat table and has a current I flowing in it At this particular place the earth's magnetic filed is `B =B_(x) hati +B_(y) hatj` How large must I be before one edge of the loop will lift from table
Repeat if ,`oversetrarr(B) = oversetrarr(B_(x)) hati + oversetrarr(B_(z)) hatk` .

Text Solution

Verified by Experts

The correct Answer is:
(a) `I = (mg)/(pi r (B_(x)^(2) +B_(y)^(2))^(1//2))` (b) `I =(mg)/(pi r B_(x))`
`oversetrarrtau_(current) = oversetrarrM xx oversetrarrB = (Ipir^(2)hatk) xxx (B_(x)hati + B_(y)hatj)`
`tau_(current)= Ipi r^(2) (B_(x)hatj -B_(y)hati)`
`tau_(currnt) =I pi r^(2) sqrt(B_(x)^(2) +B_(y)^(2))`
`tau_(mg) = tau_(current) implies mg.r. = Ipi r^(2) sqrt(B_(x)^(2) +B_(y)^(2))`
`I =(mg)/(pirsqrt(B_(x)^(2) +B_(y)^(2)))darr`
`oversetrarrtau_(current) = (Ipir^(2)hatk) xx (B_(x)hati + B_(z)hatk) =Ipi r^(2)B_(x)hatj`
`tau_(mg) = tau_(current) implies mgr =Ipir^(2) B_(x) implies I (mg)/(pirB_(x))`
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