Current I is flowing through two materials ha | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) According to Gauss's law, the flux through a closed surface is $\oint \vec{E} \cdot d\vec{A} = \frac{q_{in}}{\varepsilon_0}$.Consider a Gaussian s

Vedclass · Accepted Answer

$I \varepsilon_0 (1/\sigma_2 - 1/\sigma_1)$

Vedclass · Answer

(A) According to Gauss's law, the flux through a closed surface is $\oint \vec{E} \cdot d\vec{A} = \frac{q_{in}}{\varepsilon_0}$.Consider a Gaussian surface in the form of a cylinder enclosing the junction.The electric field in the first material is $E_1 = J/\sigma_1$ and in the second material is $E_2 = J/\sigma_2$, where $J = I/A$ is the current density.The flux through the Gaussian surface is $\Phi = E_2 A - E_1 A = \frac{q_{in}}{\varepsilon_0}$.Substituting the expressions for $E_1$ and $E_2$:$A \left( \frac{J}{\sigma_2} - \frac{J}{\sigma_1} \right) = \frac{q_{in}}{\varepsilon_0}$Since $J = I/A$, we have:$A \cdot \frac{I}{A} \left( \frac{1}{\sigma_2} - \frac{1}{\sigma_1} \right) = \frac{q_{in}}{\varepsilon_0}$$q_{in} = I \varepsilon_0 \left( \frac{1}{\sigma_2} - \frac{1}{\sigma_1} \right)$.

Current $I$ is flowing through two materials having electrical conductivities $\sigma_1$ and $\sigma_2$ respectively $(\sigma_1 > \sigma_2)$ as shown in the figure. The total amount of charge at the junction of the materials is

Similar Questions

$A$ set of $n$ equal resistors,each of value $R$,are connected in series to a battery of emf $E$ and internal resistance $R$. The current drawn is $I$. Now,the $n$ resistors are connected in parallel to the same battery. The current drawn from the battery becomes $10I$. The value of $n$ is:

In the given circuit,find $V_a - V_b$.

In the adjacent circuit,a voltmeter of internal resistance $R$,when connected across $B$ and $C$,reads $\frac{100}{3} \ V$. Neglecting the internal resistance of the battery,the value of $R$ is ................. $k \Omega$.

In the circuit shown,the cell has $emf = 10\,V$ and internal resistance $= 1\, \Omega$. Find the current through the $4\, \Omega$ resistor.

Vedclass Test Series

Exam Paper Generator

Online Exam Module