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A conducting movable rod AB lies across the frictionless parallel conducting rails in a uniform magnetic field vecB whose magnitude at t=0 is B_(0). The rod AB is given velocity v right ward and it continues to move with same velocity through out the motion [The acceleration due to gravity is along negative z-axis, i.e. vecg=10m//s^(2)(-hatk), mass of rod =m.] Which of the following graphs will be the best representation of magnitude of magnetic field versus time. |
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Answer»
`e=lBv+l(b+vt)(dB)/(dt)=0` `rArr (b+vt)(dB)/(dt)=-BV` `rArr int_(B_(0))^(B)(dB)/(B)=-vint_(0)^(t)(dt)/(b+vt)` `rArrlnB//B_(0)=-v[(1)/(v)LN((b+vt)/(b))]=ln((b)/(b+vt))` `rArr B=(B_(0)b)/(b+vt)` Second Method : So flux does not change with time, so `phi(1)=phi(t+dt)` `rArrBl(b+vt)=(B+dB)l[b+v(t+dt)]` `rArr (b+vt)dB+Bvdt=0` `rArr (dB)/(B)=-V(dt)/(b+vt)rArrB=(B_(0)b)/(b+vt)` |
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