A solid insulating sphere of radius R has a charge of Q, (Q > 0) placed on it, uniformly distributed throughout its volume. Surrounding the sphere is a spherical conducting shell with inner radius 2R and outer radius 3R and has a charge of −2Q placed on it. The sphere and the shell share the same center.

1A: Determine the magnitude of the electric field, E(r), where r is the distance from the center of the sphere

1B: Determine the electric potential, V (r), setting V (∞) = 0

3C: Graph V (r)

Two capacitors C1 = 6.8 μF, C2 = 14.6 μF are charged individually to V1 = 19.6 V, V2 = 3.5 V. The two capacitors are then connected together in parallel with the positive plates together and the negative plates together.Calculate the amount of charge (absolute value) that flows from one capacitor to the other when the capacitors are connected together. By how much (absolute value) is the total stored energy reduced when the two capacitors are connected? The final potential difference across the plates of the capacitors once they are connected was calculated to be 8.616 V

1. A 0.294 m radius, 486-turn coil is rotated one-fourth of a revolution in 3.88 ms, originally having its plane perpendicular to a uniform magnetic field. Find the magnetic field strength needed to induce an average emf of 13,000 V.

2. An American traveler in a foreign country carries a transformer to convert that country's standard 175 V to 120 V so that she can use some small appliances on her trip. What is the ratio of turns in the primary and secondary coils of her transformer?

A proton travels through uniform magnetic and electric fields. The magnetic field is in the negative x direction and has a magnitude of 3.52 mT. At one instant the velocity of the proton is in the positive y direction and has a magnitude of 2600 m/s. At that instant, what is the magnitude of the net force acting on the proton if the electric field is (a) in the positive z direction and has a magnitude of 5.40 V/m, (b) in the negative z direction and has a magnitude of 5.40 V/m, and (c) in the positive x direction and has a magnitude of 5.40 V/m?

An article presents voltage measurements for a sample of 66 industrial networks in Estonia. Assume the rated voltage for these networks is 232 V. The sample mean voltage was 231.5 V with a standard deviation of 2.19 V. Let μ represent the population mean voltage for these networks.

a) Find the P-value for testing H0 : μ = 232 versus H1 : µ ≠ 232. Round the answer to four decimal places.

b) Either the mean voltage is not equal to 232, or the sample is in the most extreme % of its distribution. Round the answer to two decimal places.

An article presents voltage measurements for a sample of 66 industrial networks in Estonia. Assume the rated voltage for these networks is 232 V. The sample mean voltage was 231.5 V with a standard deviation of 2.19 V. Let μ represent the population mean voltage for these networks.

a) Find the P-value for testing H0 : μ = 232 versus H1 : µ ≠ 232. Round the answer to four decimal places.

b) Either the mean voltage is not equal to 232, or the sample is in the most extreme % of its distribution. Round the answer to two decimal places.

You build a transformer with 100 turns of wire on side 1, and 500 turns on side 2. A) If you put a voltage of 100 V (AC) on side 1, what voltage would you get on side 2? B) If you put a voltage of 100 V (AC) on side 1 with a current of 1 Amp (AC), what current would you get on side 2? C) If you put 100 V of DC voltage on side 1, what voltage would you get on side 2?

At time t=0 a positively charged particle of mass m=5.95 g and charge q=10.8 μC is injected into the region of the uniform magnetic B=B k and electric E=−E k fields with the initial velocity v=v0 i. The magnitudes of the fields: B=0.43 T, E=722 V/m, and the initial speed v0=3.42 m/s are given.

Find at what time t, the particle's speed would become equal to v(t)=4.14·v0: t =____ seconds.

Perform a dimensional analysis to obtain an equation for rising air bubble velocity, v. What variables would v depend on; i.e. what variables would you include in your analysis?

Assume that v is a function of d (air bubble diameter). p_w (density of water), g (gravitational acceleration), and u_w (viscosity of water), and perform the dimensional analysis. How many dimensionless groups do you get (and why)? Look up the defintion of Reynolds number... Is Reynolds number of the dimensionless groups resulting from your analysis?

The enzyme fumarase catalyzes the hydrolysis of fumarate:

Fumarate(aq) + H₂O(liq) → L-maleate(aq)

The turnover number k₂ for this enzyme is 2.5 × 10³ s^-1, and the Michaelis constant is 4.2 × 10^-6 mol / L.

(a) What is the rate of fumarate conversion v if the total concentration of the enzyme is 1.0 × 10^-7 mol / Land the concentration of fumarate is 3.0 × 10^-4 mol / L?

(b) What is the ratio (v/v_max) in the conditions of question (a)?

(c) At what concentration of fumarate is (v/v_max) = 0.28?