In the figure two parallel-plate capacitors A and B are connected in parallel ac

Question

In the figure two parallel-plate capacitors A and B  are connected in parallel across a 920  V battery. Each plate has area 91.0  cm2; the plate separations are 1.00  mm. Capacitor A is filled with air; capacitor B is filled with a dielectric of dielectric constant ? = 5.60. Find the magnitude (in N/C) of the electric field within (a) the dielectric of capacitor B and (b) the air of capacitor A. What are the free charge densities ? on the higher-potential plate of (c) capacitor A and (d)  capacitor B? (e) What is the induced charge density ?' on the top surface of the dielectric?

In the figure two parallel-plate capacitors A and B are connected in parallel across a 920 V battery. Each plate has area 91.0 cm2; the plate separations are 1.00 mm. Capacitor A is filled with air; capacitor B is filled with a dielectric of dielectric constant ? = 5.60. Find the magnitude (in N/C) of the electric field within (a) the dielectric of capacitor B and (b) the air of capacitor A. What are the free charge densities ? on the higher-potential plate of (c) capacitor A and (d) capacitor B? (e) What is the induced charge density ?' on the top surface of the dielectric?

Explanation / Answer

a)

E=V/d =920/(1*10^-3)

E=920,000 V/m or 920KV/m

b)

E=920,000 V/m or 920KV/m

c)

charge denisty

sigma=eoE=(8.854*10^-12)(920,000)

sigma =8.14*10^-6 C/m^2

d)

sigma=KeoE=5.6*(8.854*10^-12)(920,000)

sigma=45.6*10^-6 C/m^2

e)

sigma' =8.14*10^-6-45.6*10^-6

sigma'=-37.46*10^-6 C/m^2 or -3.746*10^-5 C/m^2

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