91影视

1. The total number of turns of the coil is, N = 120
2. The radius of the coil is, 1.8 cm
3. The resistance is,$\mathrm{R}=5.3\mathrm{惟}$
4. The number of turns per meter is, n=220 turns/m= 22000 turns/m
5. The diameter of the solenoid is, 3.2 cm
6. The current drop from 1.5 A to 0 in time interval $鈭�t=25\mathrm{ms}$.

Find the emf induced due to the change in the magnetic flux. Now, applying Ohm鈥檚 law, find the current induced in the coil during $\mathbf{鈭�}\mathit{t}$.

Faraday'slaw of electromagnetic inductionstates, Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced in it.

Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it, provided all physical conditions and temperatures remain constant.

Formulae are as follow:

$$\begin{gathered} {桅}_B=BA \\ B={渭}_{0}in \\ 蔚=-N\frac{d{桅}_B}{dt} \\ i=\frac{\left|蔚\right|}{R} \end{gathered}$$

Where,${桅}_B$is magnetic flux, B is magnetic field, A is area, i is current, R is resistance,饾渶 is emf, Nis number of turns,饾渿₀is permeability.

From Eq.30-2, the magnetic flux is ,

${桅}_B=BA...................(30-2)$

Also, from Eq.29-23, the magnitude of the magnetic field is given by,

$B={渭}_{0}in.......................(29-23)$

According to the Faraday鈥檚 law, emf is induced due to the change in the magnetic flux is,

$蔚=-N\frac{d{桅}_B}{dt}.......................(30-5)$

Substituting Eq.30-2 in Eq.30-5,

$蔚=-NA\frac{d\left(B\right)}{dt}$

Now, substituting Eq.29-23 in Eq.30-5,
$$\begin{gathered} 蔚=-NA\frac{d\left({渭}_{0}in\right)}{dt} \\ 蔚=-Nn{渭}_{0}A\frac{di}{dt} \end{gathered}$$

But, putting $A=蟿蟿r^2$,

$蔚=-Nn{渭}_0\left(蟿蟿r^2\right)\frac{di}{dt}$

Substituting given values,

$$\begin{gathered} 蔚=-\left(120\right)\left(22000\frac{\mathrm{turns}}{\mathrm{m}}\right)\left(4\mathrm{蟿蟿}脳{10}^{-7}\mathrm{T}.\frac{\mathrm{m}}{\mathrm{A}}\right)\left[\mathrm{蟿蟿}{(0.016\mathrm{m})}^2\right]\left(\frac{1.5\mathrm{A}}{0.025\mathrm{s}}\right) \\ \mathrm{蔚}=-0.16\mathrm{V} \end{gathered}$$

According to Ohm鈥檚 law,

$$\begin{gathered} i=\frac{\left|蔚\right|}{R} \\ i=\frac{0.16V}{5.3惟} \\ i=0.030A \end{gathered}$$

Hence, the current induced in the coil during $鈭�t$is $i=0.030A$.

Therefore, by using the concept of Faraday鈥檚 law and Ohm鈥檚 law, the current induced in the coil can be determined.