A moving belt in a van de graaf generator transfers charge from one point to another. If the belt is 0.1 m. wide, moves with a velocity of 10 m/s and carries a surface charge of +10^-5 C/m^2, determine the current that this generator represents.
current=charge/sec=chargedensity*area*velocity
To determine the current generated by the van de Graaf generator, we first need to find the charge passing through the belt per unit time (the rate of charge flow), and then divide it by the time.
The rate of charge flow can be calculated by multiplying the velocity of the belt by the width of the belt and the charge density. The charge density is given as +10^-5 C/m^2.
Rate of charge flow = velocity × width × charge density
Rate of charge flow = 10 m/s × 0.1 m × + 10^-5 C/m^2
Next, we need to find the time it takes for one unit of charge to pass through the belt. The time can be calculated by dividing the width of the belt by the velocity of the belt.
Time = width / velocity
Time = 0.1 m / 10 m/s
Now we have all the information needed to calculate the current generated by the van de Graaf generator, which is the amount of charge passing through the belt per unit time.
Current = (Rate of charge flow) / (Time)
Substituting the values we calculated earlier:
Current = (10 m/s × 0.1 m × + 10^-5 C/m^2) / (0.1 m / 10 m/s)
Simplifying the equation:
Current = (10 × 0.1 × 10^-5) / 0.01
Current = 10^-4 C/s
Therefore, the current generated by this van de Graaf generator is 10^-4 C/s (or 0.1 mA).