9. A zinc wire sample at 20C is found to have resistivity p=5.9 X10% ohm-m. (a)...

 

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9. A zinc wire sample at 20°C is found to have resistivity p=5.9 X10% ohm-m. (a) Find the conductivityo. (b) An applied electric voltage drives a steady current through the zinc sample. The current density at a point in the sample is found to be J = 4 X 10 A/m². Calculate the electric field at that point. (e) The wire sample has cross- section area 4mm² = 4X10m² and length 1cm= 102m. Find the resistance of the sample. 10. A 60 Hz alternating voltage of 110V effective value is applied to a series circuit having an inductance L of 1.00H, a capacitance C of 2.00μF, and a resistance R of 400 Ohms. Calculate the: (a) Inductive reactance (b) Capacitive reactance (c) Total impedance (d) Effective current in the circuit 11. A ring of wire with radius R is centered at the origin and lies on the x-y plane, so that it's axis coincides with the z-axis. Current I flows around this circular wire loop. (a) Using the Biot-Savart law, calculate the magnetic field at the center of the loop, i.e., at the origin. (b) Using the Biot-Savart law, calculate the magnetic field at the point (0, 0, zo) on the z-axis (a point on the axis of the loop). R 12. A very long cylinder with Radius R has charge distributed throughout its volume and on its surface. The volume charge density depending on the distances from the axis of the cylinder as p = Powhere po is just a constant. The charge on the surface is uniform- the surface charge density oo is constant (a) Use Gauss's Law to find the electric field (s<R) and outside (s>R) the cylinder. Note: be clear about your choice of Gaussian surface, the flux through these surfaces, and how much charge they contain (b) Show tht the electric field has the correct discontinuity at the surface of the cylinder (s-R) 13. Find the total electric flux through a closed cylinder containing a line charge along its axis with linear charge density A = Ao(1) if the cylinder and the line charge extend from x=0 to x h. 14. A solid sphere of radius R carries a total charge Q, uniformly distributed in the volume of the sphere. (a) What is the charge density? (b) Empioy Gauss's dielectric flux theorem to calculate the electric field inside the sphere, at distance r < R from the center of the sphere. Provide a drawing showing relevant surfaces and distances. (c) What is the electric field outside the sphere, at distance r> R from the center of the sphere? (Showing a derivation is not necessary.) (d) Using your expressions for the electric field, find the electric potential V (r), outside the sphere and inside the sphere. 15. A ball of known charge q and unknown mass m, initially at rest, falls freely from a height h in a uniform electric field E that is directed vertically downward. The ball hits the ground at a speed v-2vgh. Find m in terms of E, q and g. Ч 9. A zinc wire sample at 20°C is found to have resistivity p=5.9 X10% ohm-m. (a) Find the conductivityo. (b) An applied electric voltage drives a steady current through the zinc sample. The current density at a point in the sample is found to be J = 4 X 10 A/m². Calculate the electric field at that point. (e) The wire sample has cross- section area 4mm² = 4X10m² and length 1cm= 102m. Find the resistance of the sample. 10. A 60 Hz alternating voltage of 110V effective value is applied to a series circuit having an inductance L of 1.00H, a capacitance C of 2.00μF, and a resistance R of 400 Ohms. Calculate the: (a) Inductive reactance (b) Capacitive reactance (c) Total impedance (d) Effective current in the circuit 11. A ring of wire with radius R is centered at the origin and lies on the x-y plane, so that it's axis coincides with the z-axis. Current I flows around this circular wire loop. (a) Using the Biot-Savart law, calculate the magnetic field at the center of the loop, i.e., at the origin. (b) Using the Biot-Savart law, calculate the magnetic field at the point (0, 0, zo) on the z-axis (a point on the axis of the loop). R 12. A very long cylinder with Radius R has charge distributed throughout its volume and on its surface. The volume charge density depending on the distances from the axis of the cylinder as p = Powhere po is just a constant. The charge on the surface is uniform- the surface charge density oo is constant (a) Use Gauss's Law to find the electric field (s<R) and outside (s>R) the cylinder. Note: be clear about your choice of Gaussian surface, the flux through these surfaces, and how much charge they contain (b) Show tht the electric field has the correct discontinuity at the surface of the cylinder (s-R) 13. Find the total electric flux through a closed cylinder containing a line charge along its axis with linear charge density A = Ao(1) if the cylinder and the line charge extend from x=0 to x h. 14. A solid sphere of radius R carries a total charge Q, uniformly distributed in the volume of the sphere. (a) What is the charge density? (b) Empioy Gauss's dielectric flux theorem to calculate the electric field inside the sphere, at distance r < R from the center of the sphere. Provide a drawing showing relevant surfaces and distances. (c) What is the electric field outside the sphere, at distance r> R from the center of the sphere? (Showing a derivation is not necessary.) (d) Using your expressions for the electric field, find the electric potential V (r), outside the sphere and inside the sphere. 15. A ball of known charge q and unknown mass m, initially at rest, falls freely from a height h in a uniform electric field E that is directed vertically downward. The ball hits the ground at a speed v-2vgh. Find m in terms of E, q and g. Ч

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