Faraday generates electricity using rivers!

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

Consider vertical component of the magnetic field produced by earth is \(B_v\) and the resistivity of river water is \(\rho\).

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