A structure formed from two straight conducting rods forming a right angle, is placed in a uniform magnetic field with B $$=$$ $$0.40$$ T is directed out of the page. A straight conducting bar in contact with the structure, starts at the vertex at time t $$=$$ $$0$$ and moves with a constant velocity of $$5.0$$ $$m/s$$ along them. The emf (in$$ $$V) around the triangle atthat time $$t=4.0$$ s is $$__________$$.

Question

A structure formed from two straight conducting rods forming a right angle, is placed in a uniform magnetic field with B $$=$$ $$0.40$$ T is directed out of the page. A straight conducting bar in contact with the structure, starts at the vertex at time t $$=$$ $$0$$ and moves with a constant velocity of $$5.0$$ $$m/s$$ along them. The emf (in$$ $$V) around the triangle atthat time $$t=4.0$$ s is $$__________$$.

Infinity Learn · Accepted Answer

The perpendicular length of the triangular area enclosed by the structure and bar is the same as the distance travelled by it in time $$td=vt$$, where $$v=5.0$$ $$m/s$$.Here the "base" of that triangle (the$$ distance between the intersection points of the bar with the $$structure) is $$2d$$. Thus, the area of the triangle $$isA=12($$ base $$)($$ height $$)=12(2vt)(vt)=v2t2Since$$ the field is a uniform B $$=$$ $$0.350$$ T, then the magnitude of the flux (in$$ SI $$units) isϕ$$B=BA=(0.40)(5.0)2t2=10.0t2The$$ magnitude of the emf is the (absolute$$ value $$of) Faraday's law:ε$$=d$$ϕ$$Bdt=10.0dt2dt=20.0t$$ At $$t=4.0s$$, this yields ε$$=80.0V$$

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