Chapter 16: Answer is provided, provide a step by step solution. 10/10 poinmts l

Question

Chapter 16: Answer is provided, provide a step by step solution.

10/10 poinmts l A capacitor consists of two charged disks of adius 4 m separated by a distance 2 mm see the figure The magnitude of the ha e on each disk s 45 uc consider points A C, and D inside the capacitor, as shown in the diagram. The distance 51-1.7 mm and the distance s20.6 mm. (Assume the x exis is to the right, the ty axis is up, and the z axis out.) MI4 16.6.066 (a) What is the electric field inside the capackor? -10120,,) NC (b) First, calculate the potential difference VB VA What is si along this path? 67-,0017,0,0)m What is volts (e) Next, calculate the potential difference Vc-Va What is i along this path? What is Vc VB? (d) Finally, calculate the potential difference Va What is s along this path? A-0017,.0006,0)m volts Additonal Materilas Section 16.6

Explanation / Answer

a)we know that, electric field inside the plates is:

E = sigma/e0 = Q/A e0

E = 45 x 10^-6/3.14 x 4^2 x 8.85 x 10^-12 = 101209 N/C

Its directed along x so

E = (101209,0,0) N/C

b)We know that,

E = V/d => V = Ed

d = -1.7 mm = 0.0017 m

in vector form

d = (-0.0017, 0, 0)

V(B) = 0.0017 x 101209 = 172.06 V/m

V(A) = 0

V(B) - V(A) = 172 V

c)s2 = 0.6 mm = 0.0006 m

in vector form

(0, -0.0006, 0)

V(B) = V(C) = V = 172 V

both are at same potential so the diffrence,

V(B) - V(C) = 0

d)along x,

d = 0.0017

and along y ; d = 0.006

D = (0.0017, 0.006, 0)

V(A) = 0 ; V(C) = V(B) = 172 V

V(A) - V(C) = 0 - 172 V

Hence, V(A) - V(C) = -172 V

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