• # question_answer A time varying magnetic field is present in a cylindrical region of radius R as shown in the figure. A positive charge q is taken slowly from P to Q $via$two paths-first through POQ second through PAQ. Work done by external  agent in 1stpath is W1 and through 2nd path is W2, then $\frac{{{W}_{1}}}{{{W}_{2}}}$ is                (To compute $\frac{{{W}_{1}}}{{{W}_{2}}}$, various distances and time variation of B (magnetic field) must be known.) A)  zero     B)  infinite C)  one                     D)  information insufficient

In taking charge from P to 0, one has to perform work against the force experienced by charge due to the induced electric field. The induced electric field is perpendicular to line POQ and hence ${{W}_{1}}=0$, while to compute exact value of ${{W}_{2}}$ various distances and variations of magnetic field with time must be known, but it can be predicted that ${{W}_{2}}$ is non-zero. So, ratio $\frac{{{W}_{1}}}{{{W}_{2}}}=0$.