A disc is radial crossed, through sliding contacts, by an electrical current I=4A. The disc is set perpendicullar on a magnetic field, B=20mT.The...

We'll take an infinitesimal element"dx", of radial current. This element is placed at the distance "x" from the axis of the disc.The elementary force which is acting on the current segment:

dF=l*B*dx

The power developed by this force is:

dP=dF*v=l*B*dx*2*pi*n*x

If we'll inegrate the relation above:

P=Integral (dP)=Integral(l*B*2*pi*n*x*dx) =

=l*B*2*pi*n*(x^2/2) from 0 to R=pi*n*R^2*I*B=3.14mW

The elementary moment of the elementary force dF is:

dM=dF*x=(l*B*dx*x)

M=Integral (dM)=I*B*Integral (x*dx) from 0 to R=

M=(1/2)*I*B*R^2=0.10mN*m

The result could be obtained from the relation P=M*omega

omega=angular speed

M=P/omega=(pi*n*R^2*l*B)/(2*pi*n)=(1/2)*I*B*R^2