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## Homework Statement

This is a Problem 7.7 fom Griffiths Introduction to Electrodynamics (3ed)

A metal bar of mass m slides frictionlessly on two parallel conducting rails a

distance l apart. A resistor R is connected across the rails and a uniform magnetic field B, pointing into page, fills the entire region.

If the bar moves to the right at speed v, what is the current in the resistor ?

## Homework Equations

[tex]\Phi[/tex]=BACos[tex]\phi[/tex]

[tex]E[/tex]=[tex]\frac{d\Phi}{dt}[/tex]

## The Attempt at a Solution

my reasonig is:

magnetic flux is:

[tex]\Phi[/tex]=BACos[tex]\phi[/tex]=BA=B(A0+A1).

A0 is initial surface, and A1 is surface which bar makes moving to the right with spead v.

so:

A1=x*l=v*t*l , but v is also function of t, so: A1=v(t)*t*l

I know that equation for A1 is wrong, becouse when I try to get electromotive froce

I get this:

E=d[tex]\Phi[/tex]/dt=B(0+v'(t)*t+v(t))

in solution manual it's:

E=Bl*dx/dt=Blv

Can someone explain why my reasoning is wrong, it seams logical to me.