A thin plate has the dimensions 2.80 cm times 11.2 cm and carries a charge densi

Question

A thin plate has the dimensions 2.80 cm times 11.2 cm and carries a charge density of 32.0 muC/m^2. How many elementary charge units (i.e., 1.60 times 10^-19 C) are on the entire plate? elementary charge units A +23.2 nC point charge is surrounded by a concentric conducting spherical shell of radius 2.40 cm that carries a charge of -56.5 nC. Derive expressions for the electric field as a function of radial distance both inside and outside the shell. (Use the following as necessary: epsilon_0 and r. Do not enter units in your expression. Enter the magnitude only.) E(r 2.40 cm) = N/C direction A relatively large Van de Graaff generator has a conducting sphere of radius 0.577 m. Assume that a total charge of 84.5 muC is present on the sphere. (a) What is the electric field inside the conducting sphere? N/C (b) What is the electric potential at the surface of the conductor? MV

Explanation / Answer

5) Total charge on the plate = 32*10^-6 C * 0.028*0.112 = 1.00352 × 10-7 C

Number of elementary charge = [1.00352 × 10-7] / [1.6 × 10-19] =6.272*10^11 particles

6) E(r<2.4cm) = q/(4 pi eor^2) =[23.2*10^-9/4pi]/eor^2

=1.846*10^-9/(eor^2) OUTWARD

E(r>2.4cm) = [q+Q]/(4 pi eor^2) =[(23.2-56.5)*10^-9/4pi]/eor^2

= 2.65*10^-9/(eor^2) inwards direction

7) Electric field inside = 0

Electric potental on surface = kq/r = 9*10^9*84.5*10^-6/0.577

=1318024 V = 1.318 MV

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