Question

53. Charge is distributed uniformly with a density $ ho$ throughout an infinitely long cylindrical volume of radius R. Show that the field of this charge distribution is directed radially with respect to the cylinder and that $E = frac{ ho r}{2epsilon_0}$ ($r leq R$); $E = frac{ ho R^2}{2epsilon_0 r}$ ($r geq R$).

          53. Charge is distributed uniformly with a density $
ho$ throughout an infinitely long cylindrical volume of radius R. Show that the field of this charge distribution is directed radially with respect to the cylinder and that
$E = frac{
ho r}{2epsilon_0}$ ($r leq R$);
$E = frac{
ho R^2}{2epsilon_0 r}$ ($r geq R$).

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$53. Charge is distributed uniformly with a density ho throughout an infinitely long cylindrical volume of radius R. Show that the field of this charge distribution is directed radially with respect to the cylinder and that E = frac ho r2epsilon0 (r leq R); E = frac ho R^22epsilon0 r (r geq R).$

Added by Christopher A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Adi S

06/13/2023

Step 1

First, we need to find the electric field due to a small charge element dq within the cylinder. Since the charge is uniformly distributed, we have ρ = dq/dV, where dV is the volume of the charge element. Show more…

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53. Charge is distributed uniformly with a density ρ throughout an infinitely long cylindrical volume of radius R. Show that the field of this charge distribution is directed radially with respect to the cylinder and that E = ρ r / (2 ε₀) (r ≤ R); E = ρ R² / (2 ε₀ r) (r ≥ R).

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