Question

A conducting rod of length L is moving on a horizontal smooth surface. Magnetic field in the region is vertically downward and of magnitude $B_0$. If centre of mass of the rod is translating with velocity $v_0$ and rod rotates about centre of mass with angular velocity $v_0/L$ ,then potential difference between points O and A will be

• A. $\frac{5}{8}{B}_0{V}_{0}L$
  
• B. $\frac{3}{8}{B}_0{v}_{0}L$
  
• C. $\frac{1}{8}{B}_0{v}_{0}L$
  
• D. $\frac{1}{2}{B}_0{v}_{0}L$

Answer 1

The correct option is A $\frac{5}{8}{B}_0{V}_{0}L$


Potential difference between O and A is Blv
Where v is the velocity of the mid-point of O and A
Thus, $e=B_0\left(\frac{L}{2}\right)[v_0+\frac{L}{4}\left(\frac{v_0}{L}\right)]=\frac{5B_{0}L{v}_0}{8}$