A uniform bar of length L carries a current I in the direction from point a to p

Question

A uniform bar of length L carries a current I in the direction from point a to point b (Figure 1) . The bar is in a uniform magnetic field that is directed into the page. Consider the torque about an axis perpendicular to the bar at point a that is due to the force that the magnetic field exerts on the bar.

Suppose that an infinitesimal section of the bar has length dx and is located a distance x from point a. Calculate the torque d about point a due to the magnetic force on this infinitesimal section.

Express your answer in terms of the variables I, B, x and dx.

Explanation / Answer

magnetic force on the small segment, dF = B*I*dx*sin(90)

This force acts perpendicular to I and B.

so, Torque due to this force, dT = x*dF*sin(90)

= x*B*I*dx

= B*I*x*dx <<<<<---------Answer

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