# 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 disc radius R=50mm 1. Calculate the power of...

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 disc radius R=50mm

1. Calculate the power of engine, knowing the speed is n=5rot/s.

2. Find the torque moment.

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### 1 Answer

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