A non-conducting solid cylinder of infinite length has uniform charge density ρ and radius 5R. If the electric flux through surface ABCD shown in the figure is 2θρR³/ε₀, find θ.

Question

G1 Physics · Accepted Answer

Step 1: For an infinite uniformly charged solid cylinder of radius 5R, at an outside distance r the field is E(r)=ρ(5R)²/(2ε₀r)=25ρR²/(2ε₀r). Step 2: Evaluate the flux through the indicated rectangular surface by integrating E·dA over its radial span as set by the figure. The integral gives Φ=12ρR³/ε₀. Step 3: Comparing with 2θρR³/ε₀ gives θ=6.