Question

In a certain medium, the electric potential is given by V(x)=rho0/aϵ0 ​​​(1−e⁻ᵃˣ)

where rho0​ and a are constants. Find the electric field intensity, E

Answer 1

Final Answer:
The electric field intensity E in the given medium is given by
`\(E(x) = (dV)/(dx) = (\rho_0 a)/(\varepsilon_0) e^(-ax)\).`

Step-by-step explanation:

The electric field intensity E is the negative derivative of the electric potential V with respect to position x. In this case, the electric potential is given by
`\(V(x) = (\rho_0)/(a\varepsilon_0) (1 - e^(-ax))\).`

To find
`\(E(x)\),` we take the derivative of V with respect to x:

`\[E(x) = (dV)/(dx) = (d)/(dx) \left((\rho_0)/(a\varepsilon_0) (1 - e^(-ax))\right)\]`

Using the chain rule and derivative of exponential function, we get:

`\[E(x) = (\rho_0 a)/(\varepsilon_0) e^(-ax)\]`

This expression represents the electric field intensity as a function of position x in the given medium.

Understanding the electric field intensity is crucial in electromagnetics as it describes the force exerted on a charged particle in an electric field. The exponential term in the expression indicates how the field intensity varies with the position within the medium.