1.

A conductingframe in the shape of an equilateral triangle (mass m, side a) carrying a current I is placed vertically an a horizontal rough surface (coefficient of friction is mu). The frame is free to rotate about y- axis only. A magnetic field exists such that bar(B)=-B_(0)yhat(i). Then

Answer»

The maximum value of `B_(0)` so that the FRAM does not rotate `(2mumg)/(Ia^(2))`
The maximum value of `B_(0)` so that the frame does not rotate `(mumg)/(Ia^(2))`
If seen from the top, the frame will have a tendency to rotate counter clockwise.
If seen from the top, the frame will have a tendency to rotate clockwise.

Solution :`dF` on each of the two symmetric elements
`=1xx((2dy)/(SQRT(3)))B_(0)yxx(sqrt(3))/2`
`impliestau=int_(0)^((sqrt(3)a)/2)(2B_(0)l_(y)dy)/(sqrt(3))XX((sqrt(3))/2a-y)`
`=2/(sqrt(3))IB_(0) int^((sqrt(3))/2 a) ((sqrt(3))/2a-y)ydy=(IB_(0)a^(3))/8`
`tau_(friction)=2{(mumg)/a int_(0)^(a//2) xdx}=(mumga)/4`
For the frame to rotate
`(IB_(0)a^(3))/8le(mumga)/4`
`B_(0)le(2mumg)/(Ia^(2))`


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