d1 and d2 don\'t have same thickness. lease help. Thanks 4. A parallel plate cap

Question

d1 and d2 don't have same thickness. lease help. Thanks 4. A parallel plate capacitor with square plates is filled with 2 dielectric slabs as shown in the figure below. Both slab widths span the full width of the plates, and both have the same The relative permittivities are given in the figure. A voltage of v 100 vis applied across the capacitor. (a) determine the total capacitance (b) find the magnitude of the surface charge density on each plate, p 1 and pa (c) find the magnitude of the electric field in each material, E, and E2

Explanation / Answer

a) The total capacitor can be considered as two capacitor in series. One capacitor is filled with mateial with dielectric constant r1 and other will dielectric constant r2. Then

C1 = r1 0 A/d1 = 2 × 8.85 × 10-12 × 100 × 10-4 / (1×10-3) = 0.177 nF

C2 = r2 0 A/d2 = 4 × 8.85 × 10-12 × 100 × 10-4 / (2×10-3) = 0.177 nF

So, total capacitance in series, C = C1 + C2 = 0.177 nF + 0.177 nF = 0.354 nF

b) As both the capacitors have same capacitances, the voltage drop on each capacitor will be

V1 = V2 = V/2 = 100/2 = 50V

The surface charge density on plate s1 = Q1/A = C1×V1/A = 0.177nF × 50 / (100 × 10-4) = 8.85 × 10-9 C m-2

The surface charge density on plate s2 = Q2/A = C2×V2/A = 0.177nF × 50 / (100 × 10-4) = 8.85 × 10-9 C m-2

c) The electric field in the capacitor is given by E1 = Q1/(r1× 0 × A) = C1×V1 / (r1× 0 × A) = 500 N/C

Similarly, E2 = Q2/(r2× 0 × A) = C2×V2 / (r2× 0 × A) = 250 N/C

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