An infinitely long straight wire with uniform line charge density lies at a perpendicular distance d from a point O. The total electric flux through the surface of a sphere of radius R > d centred at O, is

Step-by-step solution

Using Gauss's Law, the total electric flux through a closed surface is = q_ enclosed ₀ . The wire is at a perpendicular distance d from the center of the sphere of radius R . Since R > d , the wire intersects the sphere, forming a chord. In the right-angled triangle formed by the center of the sphere, the midpoint of the chord, and the point of intersection of the wire with the sphere, the hypotenuse is R and the perpendicular distance is d . The half-length of the wire enclosed by the sphere is R^2 - d^2 . The tot