Question

A infinitely long line of charge of linear charge density l. The potential difference between two points A and B as shown in fig. is -

• A. $\frac{\lambda}{2\pi\varepsilon_{0}}$ln 2
• B. -$\frac{\lambda}{2\pi\varepsilon_{0}}$ ln 2
• C. $\frac{\lambda}{4\pi\varepsilon_{0}}$ln 2
• D. -$\frac{\lambda}{4\pi\varepsilon_{0}}$ln 2

Answer 1

Answer: (A)

$\frac{\lambda}{2\pi\varepsilon_{0}}$ln 2

Answer 2

V_A - V_B = - $\int_{B}^{A}{\overset{\rightarrow}{E}.\overset{\rightarrow}{dr}}$

V_A - V_B = - $\int_{2r}^{r}{\frac{2\lambda}{4\pi\varepsilon_{0}r}dr}$

V_A - V_B = $\frac{2\lambda}{4\pi\varepsilon_{0}r}$ $\int_{r}^{2r}{\frac{1}{r}dr}$

= $\frac{2\lambda}{4\pi\varepsilon_{0}}$ ln $\frac{2r}{r}$

= $\frac{2\lambda}{4\pi\varepsilon_{0}}$ln 2