Chapter 26

A certain \(x\) -ray tube operates at a current of \(7.00 \mathrm{~mA}\) and a potential difference of \(80.0 \mathrm{kV}\). What is its power in watts?

A current is established in a gas discharge tube when a sufficiently high potential difference is applied across the two electrodes in the tube. The gas ionizes; electrons move toward the positive terminal and singly charged positive ions toward the negative terminal. (a) What is the current in a hydrogen discharge tube in which \(3.1 \times 10^{18}\) electrons and \(1.1 \times 10^{18}\) protons move past a crosssectional area of the tube each second? (b) Is the direction of the current density \(\vec{J}\) toward or away from the negative terminal?

An insulating belt moves at speed \(30 \mathrm{~m} / \mathrm{s}\) and has a width of \(50 \mathrm{~cm} .\) It carries charge into an experimental device at a rate corresponding to \(100 \mu\) A. What is the surface charge density on the belt?

In a hypothetical fusion research lab, high temperature helium gas is completely ionized and each helium atom is separated into two free electrons and the remaining positively charged nucleus, which is called an alpha particle. An applied electric field causes the alpha particles to drift to the east at \(25.0 \mathrm{~m} / \mathrm{s}\) while the electrons drift to the west at \(88.0 \mathrm{~m} / \mathrm{s}\). The alpha particle density is \(2.80 \times 10^{15} \mathrm{~cm}^{-3} .\) What are (a) the net current density and (b) the current direction?

A beam of \(16 \mathrm{MeV}\) deuterons from a cyclotron strikes a copper block. The beam is equivalent to current of \(15 \mu \mathrm{A}\). (a) At what rate do deuterons strike the block? (b) At what rate is thermal energy produced in the block?

A linear accelerator produces a pulsed beam of electrons. The pulse current is \(0.50 \mathrm{~A},\) and the pulse duration is \(0.10 \mu \mathrm{s}\). (a) How many electrons are accelerated per pulse? (b) What is the average current for a machine operating at 500 pulses/s? If the electrons are accelerated to an energy of \(50 \mathrm{MeV},\) what are the (c) average power and (d) peak power of the accelerator?

An electric immersion heater normally takes 100 min to bring cold water in a well-insulated container to a certain temperature, after which a thermostat switches the heater off. One day the line voltage is reduced by \(6.00 \%\) because of a laboratory overload. How long does heating the water now take? Assume that the resistance of the heating element does not change.

A \(400 \mathrm{~W}\) immersion heater is placed in a pot containing \(2.00 \mathrm{~L}\) of water at \(20^{\circ} \mathrm{C}\). (a) How long will the water take to rise to the boiling temperature, assuming that \(80 \%\) of the available energy is absorbed by the water? (b) How much longer is required to evaporate half of the water?

A \(30 \mu \mathrm{F}\) capacitor is connected across a programmed power supply. During the interval from \(t=0\) to \(t=3.00 \mathrm{~s}\) the output voltage of the supply is given by \(V(t)=6.00+4.00 t-2.00 t^{2}\) volts. At \(t=0.500 \mathrm{~s}\) find \((\mathrm{a})\) the charge on the capacitor, \((\mathrm{b})\) the current into the capacitor, and (c) the power output from the power supply.