$\frac1{4πε_0} \frac{λ}{r}$
$\frac1{4πε_0} \frac{λ}{r^2}$
$ \frac{λ}{2ε_0}$
$ \frac{λ}{2\piε_0 r}$
The correct answer is (D): $ \frac{λ}{2\piε_0 r}$
Consider an infinity long straight conductor of linear charge density
Consider a cylindrical Gaussian surface of radius r and length l.
charge enclosed by the surface
\(q=λl\)
By Gauss law
$\phi \vec{E}.ds = \frac{q}{ε_0} = \frac{λl}{ε_0} $
$ \vec{E}\phi ds= \frac{λl}{ε_0} $
$ \vec{E} \times 2\pi rl = \frac{λl}{ε_0} $
$ E = \frac{λ}{2\pi rε_0}$
LIST I | LIST II | ||
A | Gauss's Law in Electrostatics | I | \(\oint \vec{E} \cdot d \vec{l}=-\frac{d \phi_B}{d t}\) |
B | Faraday's Law | II | \(\oint \vec{B} \cdot d \vec{A}=0\) |
C | Gauss's Law in Magnetism | III | \(\oint \vec{B} \cdot d \vec{l}=\mu_0 i_c+\mu_0 \in_0 \frac{d \phi_E}{d t}\) |
D | Ampere-Maxwell Law | IV | \(\oint \vec{E} \cdot d \vec{s}=\frac{q}{\epsilon_0}\) |
List-I | List-II | ||
A | Megaliths | (I) | Decipherment of Brahmi and Kharoshti |
B | James Princep | (II) | Emerged in first millennium BCE |
C | Piyadassi | (III) | Means pleasant to behold |
D | Epigraphy | (IV) | Study of inscriptions |