Question

A square wire loop of 10 cm side lies at right angles to a uniform magnetic field of 7 T. A 10 V light bulb is in series with the loop as shown in the figure. The magnetic field is decreasing steadily to zero over the time interval $\Delta t$. For what value $\Delta t$(in ms), the bulb will shine with full brightness.

Answer 1

The electric flux is the electric field is the electric field coming out from an area on any surface of the body. The electric flux is always perpendicular to the area from which it is passing. Magnetic fields can produce an e.m.f in the circuit.

Complete step by step answer:
It is given that a square wire loop of side 10 cm is placed at right angle to a uniform magnetic field of 7 T and the circuit has a 10 V of bulb in it. The magnetic field becomes zero taking a time t and we need to find this value of time in which the bulb will shine with its full brightness.

Let us calculate the electric flux that circuit has in the circuit.
The electric flux is given by,
$\phi = \vec B \cdot \vec A$
Where $\vec B$ is the magnetic field and $\vec A$ is the area of the circuit.
$\Rightarrow \phi = \vec B \cdot \vec A$
Applying the dot product we get,
$\Rightarrow \phi = AB\cos \theta$
Put the value of the area of the circuit magnetic field and the angle between the area and the magnetic field in the above equation.
$\Rightarrow \phi = AB\cos \theta$
$\Rightarrow \phi = {\left( {0 \cdot 1} \right)^2} \cdot \left( 7 \right)\cos 90^\circ$
$\Rightarrow \phi = {\left( {0 \cdot 1} \right)^2} \cdot \left( 7 \right)\cos 90^\circ$
$\Rightarrow \phi = 0 \cdot 07N{m^2}{C^{ - 1}}$………eq. (1)
The e.m.f for an electric flux passing for a time t is given by,
$\varepsilon = \dfrac{\Phi }{t}$
Where $\varepsilon$ is e.m.f $\Phi$ is the electric flux and t is the time taken for the passing of the flux in the coil.
Replace the value of e.m.f i.e. 10 V and the value of flux from equation (1) in the above relation.
$\Rightarrow \varepsilon = \dfrac{\Phi }{t}$
$\Rightarrow 10 = \dfrac{{0 \cdot 07}}{t}$
$\Rightarrow t = \dfrac{{0 \cdot 07}}{{10}}$
$\Rightarrow t = 0.007s$
$\Rightarrow t = 7ms$
So the time for which the bulb will glow with full brightness is$t = 7ms$.

Note: The electric flux that passes through the circuit depends upon the angle which the magnetic field has with the area of the circuit. The best value of angle for the maximum passage of the electric flux from the circuit is $\theta = 90^\circ$.