Acylindrical capacitor is made of two concentric conducting cylinders. the inner cylinder has radius r1 = 19 cm and carries a uniform charge per unit length of λ = 30 μc/m. the outer cylinder has radius r2 = 75 cm and carries an equal but opposite charge distribution as the inner cylinder.
(a)use gauss’ law to write an equation for the electric field at a distance r1< r< r2from the center of the cylinders. write youranswer in terms of λ, r, and ε0.
(b)calculate the electric potential difference between the outside and the inside cylinders in v.
(c)calculate the capacitance per unit length of these concentric cylinders in f/m.
(d)calculate the energy stored in the capacitor per unit length, in units of j/m.
(e)write an equation for the energy density due to the electric field between the cylinders in terms of λ, r, and ε0.
(f)consider a thin cylindrical shell of thickness drand radius r1< r< r2that is concentric with the cylindrical capacitor. write anequation for the total energy per unit length contained in the shell in terms of λ, r, dr, and ε0