Imagine a ball heated to a temperature T. This Ball emits thermions with a current density...

Imagine a ball heated to a temperature T. This Ball emits thermions with a current density at the surface given by C , which is proportional to AG(Richardson's constant) and proportional to W(Work function) .
a) Using charge conservation,find the current density at any distance 'r' from center.
b) Using continuity equation, find the charge density p(r,t) at time 't' ; t > 0 and it is given that p(r,t=0) = 0.
c) By solving Maxwell's equations, also find the electric and magnetic field vectors .

Solutions

Expert Solution

Manojponduru answered 4 weeks ago

Next > < Previous

Related Solutions

The density of an oil mixture (mix) as a function of the temperature (T) and the...

The density of an oil mixture (mix) as a function of the temperature (T) and the mass fraction of the three components (mi) was measured and results are shown : T (K) m1 m2 m3 Pmix (kg/m3 ) 300 0 1 0 879.6 320 0 0.5 0.5 870.6 340 0 0 1 863.6 360 0.5 0 0.5 846.4 380 0.5 0.25 0.25 830.8 400 0.5 0.5 0 819.1 420 1 0 0 796 440 1 0 0 778.2 Find the...

A thin tungsten wire (i.e. a filament) is heated to a given temperature T. In the...

A thin tungsten wire (i.e. a filament) is heated to a given temperature T. In the visible range (i.e. wave length between 0.39µm and 0.77µm), Determine the following for the four cases listed below: (a) the band fraction of emitted radiation energy (b) the blackbody radiation energy emitted The four cases correspond to to following values of T: (i) T=500K (ii) T=1500K (iii)T=2500K (iv) T=3500K The melting temperature of tungsten is 3698K. Show all calculation details.

The temperature T in a metal ball is inversely proportional to the distance from the center...

The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1, 2, 2) is 120°. (a) Find the rate of change of T at (1, 2, 2) in the direction toward the point (3, 3, 4).

The temperature T in a metal ball is inversely proportional to the distance from the center...

The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1, 2, 2) is 120 degrees F . a) Find the rate of change of T at (1, 1,2) in the direction towards the point (2, 1,3). b) Show that at any point in the ball the direction of greatest increase in the temperature is given by a vector...

The temperature T in a metal ball is inversely proportional to the distance from the center...

The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1, 2, 2) is 160°. (a) Find the rate of change of T at (1, 2, 2) in the direction toward the point (3, 1, 4). (b) Show that at any point in the ball the direction of greatest increase in temperature is given by a vector that points...

Current through a heated metal wire A 39.5 m long copper wire at a temperature of...

Current through a heated metal wire A 39.5 m long copper wire at a temperature of 22.9 oC has a radius of 0.275 mm. If a potential difference of 11.8 V is applied across the length of the wire, determine the current in the wire. If the wire is heated to 90.6 oC and the 11.8 V potential difference is maintained, what is the resulting current in the wire?

Imagine you're trying to change the course of an incoming ball, heavy ball. The ball is...

Imagine you're trying to change the course of an incoming ball, heavy ball. The ball is rolling toward you, and you've got a big whiteboard that you can use to either hit the ball so it moves in the opposite direction, hold still so that it bounces off, or "catch" the ball by moving the whiteboard in the opposite direction of the ball's motion as it comes into contact with the ball. If your goal was to minimize the impact...

A gallon of water is heated-up from room temperature (20oC) to its boiling temperature of 100...

A gallon of water is heated-up from room temperature (20oC) to its boiling temperature of 100 oC at atmospheric pressure. The water is further heated and completely transforms into vapor at which point the heating is stopped. What is the temperature of the steam? A)T=100oC B) T > 100 oC C) T < 100 oC

8. A coal plant emits 0.40% SO2 by volume at a temperature of 145oC and 101.3...

8. A coal plant emits 0.40% SO2 by volume at a temperature of 145oC and 101.3 kPa from the stack. The total volume of gas emitted is 2.5 x104 m3/min. How many m3 of SO2 are emitted per minute at these conditions? How many moles of SO2 are emitted per minute at these conditions? How many kgs of SO2 are emitted per minute at these conditions? How many kgs of SO2 are emitted per minute at 25oC?

A plain carbon steel ball 2 mm in diameter is heated to 1200 K in an...

A plain carbon steel ball 2 mm in diameter is heated to 1200 K in an oven and then cooled slowly in ambient air at 300 K. The convection heat transfer coefficient between air and this steel ball is 20 W / (m2 * K). You can find the density, specific heat and thermal conductivity from the property tables attached in text book with reasonable assumptions. Please derive an equation estimating the changes of the temperature of this ball with...

Subjects