Question

A long straight rail with with 5.5 cm spacing has no friction between the rail and a conducting rod that is pulled along the top of the rail. The rail is connected at the end the rod is being pulled away from by a 250 Ohm resistor. If the rod is being pulled at a constant velocity of 37 cm/s, and there is a uniform magnetic field coming up through the rails vertically of strength 1.5T, what current is induced in the loop formed by the rod, the rails and the resistor? What direction is the current flowing in the system? Draw a diagram to indicate the direction of the field and indicate the direction of the current on this diagram.

Answer 1

Using Lenz's law

$\mathcal{E}=-\frac{\partial \Phi}{\partial t},$

Which meant Change in magnetic flux .

$\Phi =BAcos(\Theta )$

but theta=0

$\Phi =BA$

A=l*x

where l = space between rails.

$\Phi =Blx$

$\varepsilon =-\frac{d(Blx)}{dt}=Bl\frac{dx}{dt}=Blv=1.5*0.055*0.37=0.030525V$

$V=IR$

$I=\frac{V}{R}=\frac{0.030525}{250}=1.221*10^-^4 Amps$

Using right hand rule

Thumb = Velocity

Middle Finger = B Magnetic Field

Index Finger = Current = Clockwise Direction.