KVPY 2020-21 SB SX Exam Previous Papers

The circular wire in figure below encircles solenoid in which the magnetic flux is increasing at a constant rate out of the plane of the page. The clockwise emf around the circular loop is ${\mathrm{\epsilon }}_0.$ By definition a voltammeter measures the voltage difference between the two points givenby ${\mathit{V}}_{\mathit{b}}-{\mathit{V}}_{\mathit{a}}=-\underset{\mathit{a}}{\overset{\mathit{b}}{\int }}\overline{\mathit{E}}.\mathit{d}\overline{\mathit{s}}.$ We assume that a and $\mathit{b}$ are infinitesimally close to each other. The values of ${\mathit{V}}_{\mathit{b}}-{\mathit{V}}_{\mathit{a}}$ along the path 1 and ${\mathit{V}}_{\mathit{a}}-{\mathit{V}}_{\mathit{b}}$ along the path 2, respectively are