Learn Path of Least Resistance Examples Here!

A hollow, conducting sphere with an outer radius of 0.250 m and an inner radius of 0.200 m has a uniform surface charge destiny of ${\displaystyle +6.37\times {10}^{-6}\frac{C}{m^2}}$. A charge of ${\displaystyle -0.500\mu C}$ is now introduced at the center of the cavity inside the sphere. 
(a) What is the new carge density on the outside of the sphere? 
(b) Calculate the strength of the electric field just outside the sphere. 
(c) What is the electric flux through a spherical surface just inside the inner surface of the sphere?

An oil pump is drawing 44 kW of electric power while pumping oil with ρ= 860 kg/m^3 at a rate of 0.1 m^3/s. The inlet and outlet diameters of the piper are 8 cm and 12 cm, respectively. If the pressure rise of oil in the pump is measured to be 500 kPa and the motor efficiency is 90 percent, determine the mechanical efficiency of the pump.

A water pump that consumes 2 kW of electric power when operating is claimed to take in water from a lake and pump it to a pool whose free surface is 30 m above the free surface of the lake at a rate of 50 L/s. Determine if this claim is reasonable.

A well-insulated rigid tank contains 3 kg of saturated liquid-vapor mixture of water at 200 kPa. Initially, three-quarters of the mass is in the liquid phase. An electric resistance heater placed in the tank is now turned on and kept on until all the liquid in the tank is vaporized. Determine the entropy change of the steam during this process. Answer: 11.1 kJ/K

A slab of insulating material of uniform thickness d, lying between ${\displaystyle \frac{-d}{2}}$ to ${\displaystyle \frac{d}{2}}$ along the x axis, extends infinitely in the y and z directions, as shown in the figure. The slab has a uniform charge density ${\displaystyle \rho }$. The electric field is zero in the middle of the slab, at x=0. Which of the following statements is true of the electric field $E_{vec}$ at the surface of one side of the slab?

A person who starting from rest at the top of a cliff swings down at the end of a rope,releases it, and falls into the water below. There are two paths bywhich the person can enter the water. Suppose he enters the waterat a speed of 13 m/s via path 1. How fast is he moving on path 2 when he releases the rope at a height of 5.20 m above the water? Ignore the effects of air resistance.

Two resistors, A and B, are connected in parallel across a 6.0V battery. The current through B is found to be 2.0 A. When the two resistos are connected in series to the 6.0 V battery,a voltmeter connected across the resistor A measures a voltage of4.0 V. Find the resistances of A and B.

(a) Determine the electric field E at the origin O in Figure due to the two charges at A and B. (Type your answer using k for proportionality constant, Q for charge and L for the length l.)
(b) Repeat, but let the charge at B be reversed in sign.