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Electric Charges and Fields — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsElectric Charges and Fields3 Marks
Question
A long charged cylinder of linear charge density $+\lambda_1$ is surrounded by a hollow coaxial conducting cylinder of linear charge density $-\lambda_2$. Use Gauss’s law to obtain expressions for the electric field at a point (i) in the space between the cylinders, and (ii) outside the larger cylinder.
✓

Answer

As Gauss’s Law states:

$\oint\overrightarrow{E}.\vec{ds}=\frac{q}{\in_0}$

  1. $\oint\overrightarrow{E_1}.\vec{ds}=\frac{\lambda_1l}{\in_0}$

$\Longrightarrow\overrightarrow{E_1}=\frac{\lambda_1}{2\pi\in_0r_1}\hat{r_1}$

  1. $\oint\overrightarrow{E_2}.\vec{ds}=\frac{(\lambda_1-\lambda_2)l}{\in_0}$

$\Longrightarrow\overrightarrow{E_2}=\frac{(\lambda_1-\lambda_2)}{2\pi\in_0r_2}\hat{r_2}$

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