1) Two infinitely long charged cylinders are centered on the same axis. The inne

Question

1) Two infinitely long charged cylinders are centered on the same axis. The inner cylinder of radius a=3cm has a uniform linear charge density n=4.00E-10 C/m along the axis. The outer cylinder of radius b =6 cm has a uniform linear charge density -n along the axis. What is the electric potential difference between the two cylinders?

___ Volts

2?As the figure 1 shows, a ring has uniform linear charge density m=2.00E-10 C/m, the radius is R=10 cm. What is the potential at P on the central perpendicular axis through the ring? (the distance between P and the center is Z=50 cm)

___ Volts

Two infinitely long charged cylinders are centered on the same axis. The inner cylinder of radius a=3cm has a uniform linear charge density n=4.00E-10 C/m along the axis. The outer cylinder of radius b =6 cm has a uniform linear charge density -n along the axis. What is the electric potential difference between the two cylinders? 2?As the figure 1 shows, a ring has uniform linear charge density m=2.00E-10 C/m, the radius is R=10 cm. What is the potential at P on the central perpendicular axis through the ring? (the distance between P and the center is Z=50 cm)

Explanation / Answer

1)

The electric field between the cylinders is:

E = (n)/(2 pi r epsilon0)

E = (4e-10)/(2*3.1416*8.85e-12*r)

E = 7.1934/r

So

V = int{-E.dr}

V = int{-(7.1934/r) dr}

V = -(7.1934) Ln(r)

the electric potential difference between the two cylinders:

dV = -(7.1934) (Ln(0.03) - Ln(0.06))

dV = -(7.1934) (Ln(0.03/0.06))

dV = -(7.1934) (-0.69315)

dV = 4.99 Volts

2)

Q = m (2 pi R) = 2e-10 * (2*3.1416*0.10) = 0.000000000125664 C

V = k Q/sqrt(R^2 + z^2) = 9e9*0.000000000125664/(0.10*0.10+0.50*0.50)y0.5 = 2.218 Volts

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