Conductors

         

If the total charge on the surface of a conducting sphere is 2.3μC2.3 \,\mu\text{C} and the diameter of the sphere is 1.1 m,1.1\text{ m}, what is the magnitude of the electric field just outside the surface of the sphere, due to the surface charge?

The value of the permittivity constant is ε0=8.85×1012 C2/Nm2.\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.

Suppose that a charged particle is held at the center of two concentric conducting spherical shells AA and B,B, as shown in the above figure. The radius of sphere AA is rA=2 cmr_A=2\text{ cm} and that of sphere BB is rB=4 cm.r_B=4\text{ cm}. The net flux Φ\Phi through a Gaussian sphere centered on the particle is 16.0×105 Nm2/Cfor 0<r<rA+8.0×105 Nm2/Cfor rA<r<rB4.0×105 Nm2/Cfor r>rA,\begin{aligned} -16.0 \times 10^5 \text{ N}\cdot\text{m}^2\text{/C} &\text{for } 0 < r < r_A \\ +8.0 \times 10^5 \text{ N}\cdot\text{m}^2\text{/C} &\text{for } r_A < r < r_B\\ -4.0 \times 10^5 \text{ N}\cdot\text{m}^2\text{/C} &\text{for } r > r_A, \end{aligned} where rr is the radius of the Gaussian sphere. Then what are the net charges of shell AA and shell B,B, respectively?

The value of the permittivity constant is ε0=8.85×1012 C2/Nm2.\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.

If an isolated conductor has net charge +15.0×106 C+15.0 \times 10^{-6}\text{ C} and a cavity with a point charge q=+4.0×106 C,q=+4.0 \times 10^{-6}\text{ C}, what are the charge of the cavity wall qwq_w and the charge on the outer surface qs?q_s?

Consider a uniformly charged conducting sphere. If the radius of the sphere is 0.50 m0.50\text{ m} and the surface charge density is 8.40μC/m2,8.40 \,\mu\text{C/m}^2, what is the approximate total electric flux leaving the surface of the sphere?

The value of the permittivity constant is ε0=8.85×1012 C2/Nm2.\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.

If the magnitude of electric field just above the surface of a charged conducting cylinder is 2.8×105 N/C,2.8 \times 10^5 \text{ N/C}, what is the surface charge density of the cylinder?

The value of the permittivity constant is ε0=8.85×1012 C2/Nm2.\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.

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