The space between two large parallel plates i | vedclass

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Question

(C) According to the question,the space between the two large parallel plates is filled with a material of uniform charge density $\rho$. Since it is

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$-\left(\frac{\rho x^2}{2 \epsilon_0}+A x+B\right)$

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(C) According to the question,the space between the two large parallel plates is filled with a material of uniform charge density $ho$. Since it is a homogeneous medium,the potential at any point between these plates is calculated using Poisson's equation:$
abla^2 V = -\frac{ho}{\varepsilon_0}$Since we need to calculate the potential at any point along the $x$-direction,the derivatives of the potential along the $y$ and $z$ directions are zero.Therefore,the equation simplifies to:$\frac{d^2 V}{d x^2} = -\frac{ho}{\varepsilon_0}$Integrating both sides with respect to $x$:$\int \frac{d^2 V}{d x^2} dx = -\int \frac{ho}{\varepsilon_0} dx$$\frac{d V}{d x} = -\frac{ho x}{\varepsilon_0} - A$Integrating both sides again with respect to $x$:$\int \frac{d V}{d x} dx = \int \left( -\frac{ho x}{\varepsilon_0} - A ight) dx$$V = -\frac{ho x^2}{2 \varepsilon_0} - Ax - B$$V = -\left( \frac{ho x^2}{2 \varepsilon_0} + Ax + B ight)$

The space between two large parallel plates is filled with a material of uniform charge density $\rho$. Assume that one of the plates is kept at $x=0$. The potential at any point $x$ between these plates is given by (where $A$ and $B$ are constants):

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