Question

a hollow cylinder box of length 1m and area of cross - section 25cm is placed in a dimensional coordinate system the electric field the region by E is50 x cap where E is in N/C and x is in meter find net flux through the cylinder and charge enclosed by the cylinder

Answer 1

Answer:

Magnitude of electric field at A ,

E(A) = 50 * 1 = 50 N/C

Magnitude of electric field at B,

E(B) = 50*2 = 100 N/C

Electric flux, ∲ φ (A) = E. ΔS

∲ φ (A) = 50 * 25 * 10^-4 * cos 180°

∲ φ (A) = -0.125 Nm^2/C^2

∲ φ (B) = 100 * 25 *10^-4 * cos 0°

∲ φ (B) = 0.25 Nm^2/C^2

Net electric flux,

∲ φ = ∲ φ (A) + ∲ φ (B)

∲ φ = 0.125 + 0.25 Nm^2/C^2

∲ φ = 0.375 Nm^2/C^2

( ii ). By Gauss Law,

φ = ∲ E. ds = q/ε₀

0.375 = q/( 8.85 * 10^-12)

q = 0.375 * 8.85 * 10^-12 C

q = 3.3 * 10^-12 C