Category : JEE Main & Advanced
It is non-conservative and non-electrostatic in nature. Its field lines are concentric circular closed curves.
A time varying magnetic field \[\frac{dB}{dt}\] always produced induced electric field in all space surrounding it.
Induced electric field \[({{E}_{in}})\] is directly proportional to induced emf so \[e=\oint{{{{\vec{E}}}_{in}}\cdot d\vec{l}}\] ...(i)
From Faraday's second laws \[e=-\frac{d\varphi }{dt}\] ...(ii)
From (i) and (ii) \[e=\oint{{{{\vec{E}}}_{in}}.d\vec{l}}=-\frac{d\varphi }{dt}\] This is known as integral form of Faraday's laws of EMI.
A uniform but time varying magnetic field B(t) exists in a circular region of radius 'a' and is directed into the plane of the paper as shown, the magnitude of the induced electric field \[({{E}_{in}})\] at point P lies at a distance r from the centre of the circular region is calculated as follows.
So \[\oint{{{{\vec{E}}}_{in}}d\vec{l}}=e=\frac{d\varphi }{dt}=A\frac{dB}{dt}\] i.e. \[E(2\pi r)=\pi {{a}^{2}}\frac{dB}{dt}\]
where \[r\ge a\] or \[E=\frac{{{a}^{2}}}{2r}\frac{dB}{dt}\]; \[{{E}_{\mathbf{in}}}\propto \frac{1}{r}\]
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