Faraday generates electricity using rivers!

Electricity and Magnetism Level 3

The figure shows an apparatus suggested by Faraday to generate electric current from a flowing river. Two identical conducting plates of length a a and width b b are placed parallel facing one another on opposite sides of the river flowing with velocity u u at a distance d d apart. Now both the plates are connected by a load resistance R R . Then the current through the load R R is?

Consider vertical component of the magnetic field produced by earth is B v B_v and the resistivity of river water is ρ \rho .

B v u d R + ρ d a b \large \frac{B_v ud}{R+ \frac{\rho d}{ab}} None of These B v u b R + ρ d a b \large \frac{B_v ub}{R+ \frac{\rho d}{ab}} B v u b R \large \frac{B_v ub}{R}

Nishant Rai by Nishant Rai , 25, India

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1 solution

Tanishq Varshney
May 30, 2015

The river can be considered as large number of rods of length d d connected in parallel.

Emf of each rod is B v u d B_{v}ud since all rods are in parallel so the equivalent emf is B v u d B_{v}ud the internal resistance of river is r e s i s t i v i t y × l e n g t h A r e a o f c r o s s − s e c t i o n resistivity\times \frac{length}{Area~of~cross-section}

which is equal to ρ d a b \frac{\rho d}{ab}

now current I = E m f l o a d r e s i s t a n c e + i n t e r n a l r e s i s t a n c e I=\frac{Emf}{load resistance ~ +~ internal ~resistance}

SO the answer is I = B v u d R + ρ d a b \huge{I=\frac{B_{v}ud}{R+\frac{\rho d}{ab}}}

7 Helpful 0 Interesting 0 Brilliant 0 Confused

What about the capacitance of the conducting plates...??? and the dielectric constant of the water??
It should behave like a RC circuit and eventually the current should stop. Tanishq Varshney Nishant Rai

Rohit Gupta - 6 years ago

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May be considering at t = 0 t=0

Tanishq Varshney - 6 years ago

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@Tanishq Varshney in steady state the current should be zero..!! As the voltage produced is constant.!!

Rohit Gupta - 6 years ago

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