Consider a long straight wire with uniform linear charge density lambda According to Gausss theorem ...........

Physics (CUET) Electrostatics

Consider a long straight wire with uniform linear charge density \( \lambda \). According to Gauss's theorem, the electric field at a distance \( r \) from the wire is given by:

(i) electric flux depends on the charge enclosed.

(ii) Gauss's law relates electric field to electric flux.

(iii) symmetry allows simplification of electric field calculation.

E = \( \frac{\lambda}{2\pi\varepsilon_0r} \) radially outward

E = \( \frac{\lambda}{4\pi\varepsilon_0r^2} \) radially inward

E = \( \frac{\lambda}{\pi\varepsilon_0r} \) along the wire

E = \( \frac{\lambda r}{\varepsilon_0} \) exponentially decreasing

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Explanation:

The electric field due to an infinitely long straight wire with linear charge density \( \lambda \) is derived using Gauss's law which states that the electric flux through a closed surface is proportional to the charge enclosed.

The correct expression is \( E = \frac{\lambda}{2\pi\varepsilon_0r} \), reflecting the radial symmetry and 1/r dependence.

Option 2 describes a 1/r² dependence which is incorrect for a line charge.

Option 3 addresses a direction along the wire, which contradicts the symmetry and radial nature of the field.

Option 4 suggests an exponential behavior, which is not applicable here.