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) \[Bv\,\ell +B\,\omega \,\,{{\left( \frac{\ell }{2} \right)}^{2}}\]
Correct Answer: A
Solution :
Point P is at instantaneous rest, |
\[{{\varepsilon }_{1}}=\,\,|{{v}_{P}}-{{v}_{A}}|\,\,=\frac{1}{2}B\omega \,\,{{\left( \frac{\ell }{2}+\frac{v}{\omega } \right)}^{2}}\] |
\[{{\varepsilon }_{2}}=\,\,|{{v}_{P}}-{{v}_{B}}|\,\,=\frac{1}{2}B\omega \,\,{{\left( \frac{\ell }{2}-\frac{v}{\omega } \right)}^{2}}\] |
\[|{{v}_{A}}-{{v}_{B}}|\,\,={{\varepsilon }_{1}}-{{\varepsilon }_{2}}\] |
\[|{{v}_{A}}-{{v}_{B}}|\,\,=B\ell v\] |
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