The electric potential at the centre of two concentric half rings of radii $R_1$ and $R_2$, having same…

The electric potential at the centre of two concentric half rings of radii $R_1$ and $R_2$, having same linear charge density ' $\lambda$ ' is ( $\varepsilon_0=$ permittivity of free space $)$
  1. $\frac{2 \lambda}{\varepsilon_0}$
  2. $\frac{\lambda}{2 \varepsilon_0}$
  3. $\frac{\lambda}{4 \varepsilon_0}$
  4. $\frac{\lambda}{\varepsilon_0}$

Solution

$\begin{aligned} & \mathrm{V}_1=\frac{1}{4 \pi \varepsilon_0} \times \frac{\lambda\left(\pi \mathrm{R}_1\right)}{\mathrm{R}_1} \\ & \mathrm{~V}_2=\frac{1}{4 \pi \varepsilon_0} \times \frac{\lambda\left(\pi \mathrm{R}_2\right)}{\mathrm{R}_2} \\ & \mathrm{~V}_{\mathrm{net}}=\mathrm{V}_1+\mathrm{V}_2=\frac{1}{4 \pi \varepsilon_0} \times \pi \lambda \times 2=\frac{\lambda}{2 \varepsilon_0}\end{aligned}$ .

Asked in: MHT CET 2024 (04 May Shift 1)

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