91影视

i) Emf of the battery is,${蔚}_{battery}=6.00渭V$

ii) Wire loop area,$A=5.0c{m}^2$

iii) Time interval t = 10 s to t = 20 s

iv) Fig.30-37

v) The field magnitude is B = at

vi) The vertical axis scale is set by$i_s=2.0mA$

vii) The horizontal axis scale is set by$t_s=30s$ .

Applying Ohm鈥檚 law, find the value of resistance and using this value offind the value of inducedemf during$\mathbf{10}\mathit{s}\mathbf{<}\mathit{t}\mathbf{<}\mathbf{20}\mathit{s}$. Using Eq.30-2 in Eq.30-4, find theconstantin the equation for the field magnitude.

Faraday's law 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:

$$\begin{gathered} i=\frac{{蔚}_{battery}}{R} \\ {蔚}_{induced}=iR-{蔚}_{battery} \\ {桅}_B=BA \\ {蔚}_{induced}=-\frac{d{桅}_B}{dt} \end{gathered}$$

Where,${桅}_B$is magnetic flux, B is magnetic field, A is area, i is current, R is resistance, 饾渶 is emf.

From Fig.30-37(b), at t = 0 , i = 0.0015A .

Applying Ohm鈥檚 law, the current i is given by,

$i=\frac{{蔚}_{battery}}{R}$

Therefore, the resistance is given by,

$$\begin{gathered} R=\frac{6.00脳{10}^{-6}V}{0.0015A} \\ R=0.0040惟 \end{gathered}$$

Now, during$10s<t<20s$ , the value of the current is ,

$i=\frac{\left({蔚}_{battery}+{蔚}_{induced}\right)}{R}$

Therefore, the induced emf is,

${蔚}_{induced}=iR-{蔚}_{battery}$

From Fig.30-37(b) , i = 0.0050A

$$\begin{gathered} {蔚}_{induced}=\left(0.00050A\right)\left(0.0040惟\right)-\left(6.00脳{10}^{-6}V\right) \\ {蔚}_{induced}=-4.00脳{10}^{-6}V \end{gathered}$$

Now, from Eq.30-2, magnetic flux is,

${蠒}_B=BA................................................................\left(30-2\right)$

According to Faraday鈥檚 law, the induced emf is,

${蔚}_{induced}=-\frac{d{桅}_B}{dt}..............................................................\left(30-4\right)$

Putting Eq.30-2,

$$\begin{gathered} {蔚}_{induced}=-\frac{d\left(BA\right)}{dt} \\ {蔚}_{induced}=-A\frac{dB}{dt} \end{gathered}$$

But,

$$\begin{gathered} \frac{dB}{dt}=a \\ {蔚}_{induced}=-Aa \end{gathered}$$

Therefore, the value of is,

$$\begin{gathered} a=-\frac{{蔚}_{induced}}{A} \\ a=-\frac{\left(-4.00脳{10}^{-6}V\right)}{\left(5.0脳{10}^{-4}{m}^2\right)} \\ a=0.0080T/s \end{gathered}$$

Hence, the value of constant a is 0.0080 T/s .

Therefore, by using the concept of Faraday鈥檚 law and Ohm鈥檚 law, the value of constant a can be deteremined.