The magnetic force on the electron is:

where q is the electron charge, v the electron speed, B the magnetic field intensity and

is the angle between v and B. Since the electron is traveling perpendicular to the magnetic field,

, so we can write

This force acts as centripetal force of the motion,

, where m is the electron mass and r the radius of the circular orbit. So we can write:

and by re-arranging this equation, we find the radius of the circular orbit, r:
Answer:

Explanation:
The formula for the surface of the circle is:

The rate of change of the spill area is obtained by deriving the previous formula in terms of time:

Finally, variables are replaced by known data:


Newton's second law states that the force applied to an object is equal to the product between the mass m of the object and its acceleration a:

Using

and

, we can find the value of the force applied to the roller-blade to obtain this acceleration:
Answer:
the difference is due to resistance tolerance
Explanation:
In mathematical calculations, either done by hand or in a computer program, the heat taken from the resistors is the nominal value, which is the writing in its color code, so all calculations give a result, but the Resistors have a tolerance, indicated by the last band that is generally 5%, 10%, 20% and in the expensive precision resistance can reach 1%.
This tolerance or fluctuation in the resistance value is what gives rise to the difference between the computation values and the values measured with the instruments, multimeters.
Another source of error also occurs due to temperature changes in the circuit that affect the nominal resistance value, there is a very high resistance group that indicates the variation with the temperature, they are only used in critical circuits, due to their high cost
In summary, the difference is due to resistance tolerance.
(a) 423 J
The power of the battery is the ratio between the total energy stored (E) and the time elapsed (t):

However, the power is also the product of the voltage (V) and the current (I):

Linking the two equations together,

Since we know:
V = 9.0 V

We can calculate the total energy:

(b)
dollars
The battery has a total energy of E = 423 J. (2)
1 Watt (W) is equal to 1 Joule (J) per second (s):

so 1 kW corresponds to 1000 J/s:

Multiplying both side by 1 hour (1 h):

and
, so

So we find the conversion between kWh and Joules. So now we can convert the energy from Joules (2) into kWh:

And since the cost is $0.0660 per kilowatt-hour, the total cost will be
dollars