Two straight conducting rails form an angle of 110degree where their ends are jo

Question

Two straight conducting rails form an angle of 110degree where their ends are joined, as shown, and a constant magnetic field of 352mT points out of the page. A conducting bar in contact with the rails and forming an isosceles triangle with them starts at the vertex (where the rails come together at t-0), and then moves to the right with a constant velocity of 5.21m/s. In which direction will the induced current flow? What is the rate at which the area of the triangle is changing, as a function of time? In other words, what is dA/dt? Remember that the velocity is the rate at which d, the distance between the vertex and the vertical bar, is increasing, so try to get the area as a function of d. What is the induced emf in the bar/rails as a function of time? You can assume that Area=0 at t=0. When will the induced emf be 56.8V?

Explanation / Answer

a. magnetic flux through the inside of the triangle is increased along out of the page. So, From lens law

current is induced which opposes the flux increase. From right hand rule

current flows clockwisely(seen from above)

b.let x b the perpendicular distance from the vertex to rod.

base length(rod length in the triangle)= 2*x*tan(55)=2.856*x =take as l

Area=x*l/2 = 1.428*x2

dA/dt= 2.856*x*v=14.88*x; but x=v*t

So, dA/dt=77.524*t

c. flux(F)= B.A

from faradays law, emf= -dF/dt= B*dA/dt =27.288*t

d.56.8=27.288*t;

t= 2.08 s

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