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As a result of change in the magnetic flux linked to the closed loop shown in the figure, an e.m.f. V volt is induced in the loop. The work done (joules) in taking a charge Q coulomb once along the loop is -
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A
QV
B
QV/2
C
2QV
D
Zero
Detailed Solution
A changing magnetic flux produces an induced electric field, whose lines are closed loops. This field is non-conservative.
The induced emf is the line integral of this field around the loop: $\oint \vec{E}\cdot d\vec{l} = V$
The force on the charge is $\vec{F} = Q\vec{E}$, and the work done in a small displacement is $dW = \vec{F}\cdot d\vec{l}$.
$W = \oint Q\vec{E}\cdot d\vec{l} = Q\oint \vec{E}\cdot d\vec{l}$
$\Rightarrow W = QV$
Unlike an electrostatic field, the induced field does non-zero work around a closed loop.
The induced emf is the line integral of this field around the loop: $\oint \vec{E}\cdot d\vec{l} = V$
The force on the charge is $\vec{F} = Q\vec{E}$, and the work done in a small displacement is $dW = \vec{F}\cdot d\vec{l}$.
$W = \oint Q\vec{E}\cdot d\vec{l} = Q\oint \vec{E}\cdot d\vec{l}$
$\Rightarrow W = QV$
Unlike an electrostatic field, the induced field does non-zero work around a closed loop.