A metallic rod of length ' a ' is rotated with an angular frequency of 0.2 ~rads ⁻¹ about an axis normal to the rod passing through its one end. A constant and uniform magnetic field of ' B ' T parallel to the axis exists everywhere. The emf developed across the ends of the rod is

Step-by-step solution

The motional electromotive force (emf) induced in a rod of length a rotating with angular velocity in a uniform magnetic field B perpendicular to the plane of rotation is given by the integral of d = B v dr , where v = r . The emf E is calculated as: E = ₀^ a B r dr E = B [ r^2 2 ]₀^ a E = 1 2 B a^2 Given the angular frequency = 0.2 rad s ⁻¹ , substitute this value into the expression: E = 1 2 B 0.2 a^2 E = 0.1 B a^2 E = 1 10 B a^2 = B a^2 10 Answer: Ba ^2 10