Question

A rod ab of lenght l is rotted with ontant anguar velocity w about an ais

Answer 1

Answer:

Motional EMF induced in a conductor of length L moving in magnetic field is given by equation

EMF = vBLEMF=vBL

now lets take a small part of length "dx" which is at distance"x" from the hinge point

the speed of the point is given by

v = x\omegav=xω

now the motional emf in that small part of the rod will be

EMF =_{x=L/2}^{x=L}\int vBdxEMF=

x=L/2

x=L

∫vBdx

EMF = _{x=L/2}^{x=L}\int x\omega BdxEMF=

x=L/2

x=L

∫xωBdx

EMF = \frac{(L^2 - (L/2)^2)}{2} \omega BEMF=

2

(L

2

−(L/2)

2

)

ωB

EMF = \frac{3B \omega L^2}{8}EMF=

8

3BωL

2

so above is the induced EMF frm centre of rod to end of rod