• # question_answer A metal rod of length  moving with an angular velocity  and velocity of its centre is v. Find potential difference between points A and B at the instant shown in figure. A uniform magnetic field of strength B exist perpendicular to plane of paper: A) $B\,v\,\ell$ B) $Bv\ell +\frac{1}{2}B\omega \,{{\ell }^{2}}$ C) $B\omega \,\ell -\frac{1}{2}B\omega \,{{\ell }^{2}}$ D) $Bv\,\ell +B\,\omega \,\,{{\left( \frac{\ell }{2} \right)}^{2}}$

 Point P is at instantaneous rest, ${{\varepsilon }_{1}}=\,\,|{{v}_{P}}-{{v}_{A}}|\,\,=\frac{1}{2}B\omega \,\,{{\left( \frac{\ell }{2}+\frac{v}{\omega } \right)}^{2}}$ ${{\varepsilon }_{2}}=\,\,|{{v}_{P}}-{{v}_{B}}|\,\,=\frac{1}{2}B\omega \,\,{{\left( \frac{\ell }{2}-\frac{v}{\omega } \right)}^{2}}$ $|{{v}_{A}}-{{v}_{B}}|\,\,={{\varepsilon }_{1}}-{{\varepsilon }_{2}}$ $|{{v}_{A}}-{{v}_{B}}|\,\,=B\ell v$