The induced emf (pot diff) produces at the ends of the conductor due to the motion of the conductor across the magnetic field is called motional emf.
Consider a conducting rod of length L placed on two parallel metal rails separated by a distance L A galvanometer is connected between the ends c and d of the rails. This forms a complete conducting loop abcda. A uniform magnetic field B is applied and directed into the paper.
The galvanometer shows no current in the loop when the rod is at rest. when the rod is pulled to the right with constant velocity V, the galvanometer shows current in the loop. This shows that the induced current produces due to the motion of the conducting rod across the magnetic field. the moving rod acts as a source of emf ε.
ε=Vb-Va= ∆V → eq 1
When the rod moves, a change q within the road also moves with the same velocity v in the magnetic field B and experiences a force given by
F=q (V × B) → eq 2
The magnitude of the force will be
F=qVB Sin θ
The angle θ between v and d b is 90°.
F=qVB Sin 90°
F=qVB (1) ∴Sin 90°=1
F=qVB → eq 3
According to the RH rule, F will be directed from a to b in the rod and produces electric field e along the rod; Its magnitude is given by
E=F⁄q → eq 4
Putting the value of F from eq. 3 in eq. 4.
E=VB → eq 5
We know that electric intensity equals the negative of the potential gradient.
E= – ∆L/L=-ε/L → eq 6
Comparing eq 5 and eq 6 we get,
-ε/L=VB → ε=-VBL → eq 7
Then the magnitude of motional emf is given by
ε=VBL Sin θ → eq 8
eq 8 shows that E = 0 When V = 0
this gives no motional emf produced in the rod at rest. It can be increased by increasing the speed of the rod and using a stronger magnetic field.