91影视

$$\begin{gathered} \mathrm{B}=\mathrm{at},\mathrm{t}\mathrm{is}\mathrm{in}\mathrm{seconds}\mathrm{and}B\mathrm{is}\mathrm{in}\mathrm{Tesla} \\ {E}_s=300\mathrm{渭狈}/\mathrm{C} \\ {\mathrm{r}}_{\mathrm{s}}=4.00\mathrm{cm} \end{gathered}$$

Use Faradays law of electromagnetic induction which relates line integral of electric field with rate of change of magnetic flux. As the rate of change of magnetic field is given. solve for constant.

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

Formulae are as follow:

$$\begin{gathered} {\stackrel{,}{o}}_{ind}=\frac{d{蠒}_B}{dt}=鈭�\stackrel{鈫�}{E}.d\stackrel{鈫�}{s} \\ d{蠒}_B=\stackrel{鈫�}{B}.d\stackrel{鈫�}{A} \end{gathered}$$

Where,${\mathrm{桅}}_{\mathrm{B}}$ is magnetic flux, B is magnetic field, A is area,饾渶 is emf, E is electric field.

Here,

$-\frac{d{蠒}_B}{dt}=鈭�\stackrel{鈫�}{E}.d\stackrel{鈫�}{s}$

Considering the magnitude of above equation,

$$\begin{gathered} \frac{d{蠒}_B}{dt}=鈭�\stackrel{鈫�}{E}.d\stackrel{鈫�}{s}=2蟿蟿rE \\ \frac{d}{dt}\left(B蟿蟿r^2\right)=E.2蟿蟿r \\ 蟿蟿r^2.\frac{dB}{dt}=E.2蟿蟿r \\ \frac{dB}{dt}=\frac{d}{dt}\left(at\right)=a \\ 蟿蟿r^2.a=E.2蟿蟿r \\ \frac{a}{2}=\frac{E}{r} \end{gathered}$$

From the plot given in the problem , the slope is,

$$\begin{gathered} \frac{E_s}{r}=\frac{300脳{10}^{-6}}{2脳{10}^{-2}}=1.5脳{10}^{-2} \\ \frac{a}{2}=\frac{E}{r}=1.5脳{10}^{-2} \\ a=3脳{10}^{-2}\mathrm{T}/\mathrm{s} \end{gathered}$$

Unit can be checked from the equation, B = at

Hence, the value of constant a is , $a=3脳{10}^{-2}\mathrm{T}/\mathrm{s}$.

Therefore, the constant a is determined by using Faraday鈥檚 law and graph of electric field vs distance.