A copper rod is moved in a magnetic field. The charge developed across its ends will be proportional to
A copper rod is moved in a magnetic field. The charge developed across its ends will be proportional to
magnetic flux
rate of change of magnetic flux
$1 /$ velocity of the rod
$1 /$ magnitude of the magnetic field
Solution
When a copper rod is moved in magnetic field, an emf is induced in such a way that current induced will try to oppose the motion of the rod.
As we know,
$
\begin{array}{lll}
& e \propto \frac{d \phi}{d t} & \\
\Rightarrow & i R \propto \frac{d \phi}{d t} & (\because e=i R) \\
\Rightarrow & \frac{d Q}{d t} \times R \propto \frac{d \phi}{d t} & \left(\because i=\frac{d Q}{d t}\right) \\
\Rightarrow & \frac{d Q}{d t} \propto \frac{d \phi}{d t} &
\end{array}
$
Hence, charge developed across the ends of the rod will be proportional to rate of change of magnetic flux