Question

Fm=Fc question regarding graphs

Answer 1

if the speed of an electron increases then does the radius of its curved path also increase?

Answer 2

looking like this?

Answer 3

the electron is moving in a magnetic field? or somewhere else ?

Answer 4

magnetic!

Answer 5

if u consider it moving in a magnetic field then it will feel two kind of forces -
\[(1) centripetal ~force\\(2)lorentz~force\]
and they will balance each other to establish equilibrium--
centripetal force on the electron will be due to circular motion
\[F_{centripetal}=\frac{ mv^2 }{ r }\\where\\v=velocity ~of ~the ~electron\\r=radius ~of ~the~path\]
and the lorentz force will be--
\[F_{lorentz}=Q*(BXv)=QBv\\Q=charge\\B=magnetic field ~flux\\v=velocity\]
so for equilibrium--
\[F_{centripetal}=F_{lorentz}\\ \frac{ mv^2 }{ r }=QBv\\mv=QBr\\so ~we~can~see~r~(radius ~of ~the~path)~~is proportional ~with~the ~velocity\]so graph will look like

Answer 6

got this?

Answer 7

ok so what you said "we can see r......... with velocity" could you explain what you did with the formula and why it would be proportional?

Answer 8

look the final expression we got is
\[mv=QBr\]
right?

Answer 9

so from here
\[v=\frac{ QBr }{ m }=(\frac{ QB }{ m})r=K*r\\where~~K= A~~constant ,\]

Answer 10

so from here cant we say that v is proportional to r ?

Answer 11

oh ok ok thnks

Answer 12

np :)

Answer 13

OH WAIT @sidsiddhartha

Answer 14

my friend said that

Answer 15

it can also be this but that means its not directly proportional though