A metallic rod of length 3.0 ~m is hinged at one end and rotated at a constant angular frequency of 100 ~rad/s in a uniform magnetic field that is perpendicular to the plane of rotation. If the induced electromotive force developed across the ends of the rod is 90 ~V , what is the magnitude of the uniform magnetic field?

Step-by-step solution

The motional emf induced across the ends of a rod of length L rotating with angular velocity in a perpendicular magnetic field B is given by: = 1 2 B L^2 Rearranging the formula to solve for the magnetic field B , we get: B = 2 L^2 Given values are: = 90 ~V = 100 ~rad/s L = 3.0 ~m Substituting these values into the rearranged equation: B = 2 90 100 (3.0)^2 B = 180 100 9 B = 180 900 = 0.2 ~T If the factor of 1 2 is forgotten, the result would incorrectly be 0.1 ~T . If the length is not squared, the result would inc