# why resistivity of metals increases on applying magnetic field??

Nicho priyatham
625 Points
8 years ago
Im not sure of your level so I will keep things fairly basic.
picture a wire going horizontal
______________________
.....- >
- >.........- >
...........->
....- >
________________________

This is for example only not necessarily will the electrons be flowing all through the conductor from outside to inside
without a magnetic field they are free to move anywhere in the conductor and they move horizonally basically (on average)
When you have an electron moving in a magnetic field though there is a force generated.
F = qv x B
.. these are all vectors F points 90 degs or pi/2 rads to both v and B
say v is positive y direction across the page
and say B points out of the page towards you on the positive x axis
and say e is the charge of one proton
then according to the equation
F = -ev x B
F = -Z
since the right hand rule says the fingers curl from -ev vector to the B vector shows the direction we would hold the hand upward with fingers pointing towards you and curling counter clockwise.
and the thumb would point upward.
the -ev vector is negative to the direction of the v vector so it points
because v vector
-------> is that way
and the B vector points out of the page at your face
so the force is UP
now what does this mean.
this means that the electrons flowing to the right of the page will be pushed UPWARD toward the top of the conductor
_______________________________
-e......-e........-e.......-e
....................-e
.........-e
-e
_________________________________

see how all the electrons would be crowded up to the top of the conductor and there for would start hitting each other more.
This crowded situation creates more resistance in the wire because the electrons can go less forward before running into another electron
I hope that helps explain why the resistivity increases in a metal thats in a magnetic field