Conveying Current Physics

A conveyor belt of width w=10cm has a surface containing a layer of electrons with an area number density of 10 000mm−2. The conveyor belt is moving at a speed v=5.0ms−1.At a certain point there is a wire brush that collects all of the electrons on the belt and transports them away as electric current. What is the magnitude of the electric current through the wire brush?

if you do know how please could you show the working so that I can learn the method.

Polite advice: Physics is not about 'learning the method'.

You will never get beyond an average 3/4/5 grade if you cannot break down a problem and understand the concepts in order to work out how to solve the problem on your own.

Having said that, you need to understand and remember some basic principles:

a) What an electric current is and how that relates to charge carrying particles, specifically electrons and protons.

b) Charge is measured in Coulombs. There are 6.24x10¹⁸ electrons in 1 Coulomb of charge.

c) Current is measured in Amperes and is the number of charge carrying particles passing a given point in one second.

i.e 1 Ampere equals 1 Coulomb of charge per second.

Putting this together to answer the question, the belt is 10cm wide and is moving at 5 metres per second.

So the total surface area of the belt passing under the brush is:

0.1 x 5 = 0.5 sq metres per second = 0.5 m²s^-1

But the area density of electrons on the belt is 10000 per square mm

So first convert 0.5m² to mm² (there are 1000x1000 = 1x10⁶ mm² in 1m²)

0.5m²s^-1 = 0.5 x 1x10⁶ = 5x10⁵ mm²s^-1

Then multiply that by the area density of electrons:

5x10⁵ x 10x10³ = 5x10⁹ electrons per second passing under the belt.



Finally, convert that to an electric current given in amperes per second:

5x10⁹ / 6.24x10¹⁸ = 0.8013^-9 Amps per second

= 8.0x10^-10 As^-1 (2 sd)

Is there no short way of doing this?