Final answer:
The electric flux across a spherical surface centered at the origin with a uniform line charge along the y-axis is (2Rλ)/ε₀.
The correct option a. is 2Rλ/ε₀
Step-by-step explanation:
The electric flux across a spherical surface centered at the origin with radius R is given by the equation Φ = q/ε₀, where q is the total charge enclosed by the surface and ε₀ is the permittivity of free space. In the given problem, we have a uniform line charge with linear density λ along the y-axis. To find the flux across the spherical surface, we need to determine the total charge enclosed by the surface.
The total charge enclosed by the spherical surface is the charge contained within a length 2R along the y-axis, which is equal to 2Rλ. Therefore, the flux across the spherical surface is Φ = (2Rλ)/ε₀.
The correct option for the flux crossing the spherical surface is 2Rλ/ε₀, so the answer is (a).