1.

A conducting frame I the shape of an equilateral Delta (mass m, side a) carrying a current l 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 vecB=-B_(0)yhati. Then

Answer»

The maximum VELUE of `B_(0)` so that the frame 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 hace 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
`=Ixx((2dy)/(SQRT(3)))B_(0)Yxx(sqrt(3))/(2)`
`impliestau=int_(0)^(sqrt(3)a)/(2))((2B_(0)I_(y)dy)/(sqrt(3)))XX((sqrt(3))/(2)a-y)`
`=(2)/(sqrt(3))IB_(0)int^((sqrt(3))/(2)a)((sqrt(3))/(2)a-y)ydy=(IB_(0)a^(3))/(8)`
`tau_("friction")=2{(mumg)/(a)int_(0)^((a)/(2))xdx}=(muga)/(4)`
For the frame to rotate
`(IB_(0)a^(3))/(8)lt(mumga)/(4)`
`impliesB_(0)LE(2mumga)/(4)`
`impliesle(2mumg)/(Ia^(2))`


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