Physics

Physics · electromagnetism

Problem

2. The potential due to the line charge could be written as V(r)=f(r)+K,V(r)=f(r)+K, where KK is a constant. Determine f(r)f(r). Given constants: A system consisted of two conductor bodies is immersed in a uniform dielectric and weakly conducting liquid. When a constant voltage difference is applied between both conductors, the system has both electric and magnetic fields. In this problem we will investigate this system. Context question: 1. First consider an infinitely long line with charge per unit length λ\lambda in vacuum. Calculate the electric field E(r)\mathbf{E}(\mathbf{r}) due to the line. Context answer: E=r^λ2πϵ0r\mathbf{E}=\hat{r} \frac{\lambda}{2 \pi \epsilon_{0} r}
Intuitive explanation

The potential is related to the electric field through integration: V(r)=−∫E⋅drV(r) = -\int \mathbf{E} \cdot d\mathbf{r}. Since you already know the radial electric field from the line charge, integrate it from some reference point to find how the potential varies with distance rr. The constant KK represents your choice of where to set the zero of potential—it's arbitrary, so focus on finding the functional form f(r)f(r) that depends on rr.

Intuitive explanation

The potential is related to the electric field through integration: V(r)=−∫E⋅drV(r) = -\int \mathbf{E} \cdot d\mathbf{r}. Since you already know the radial electric field from the line charge, integrate it from some reference point to find how the potential varies with distance rr. The constant KK represents your choice of where to set the zero of potential—it's arbitrary, so focus on finding the functional form f(r)f(r) that depends on rr.

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