An object is moving in a straight line at constant speed. A resultant torce begins to act upon
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The propagation errors we can find the uncertainty of a given magnitude is the sum of the uncertainties of each magnitude.
Δm = ∑
Physical quantities are precise values of a variable, but all measurements have an uncertainty, in the case of direct measurements the uncertainty is equal to the precision of the given instrument.
When you have derived variables, that is, when measurements are made with different instruments, each with a different uncertainty, the way to find the uncertainty or error is used the propagation errors to use the variation of each parameter, keeping the others constant and taking the worst of the cases, all the errors add up.
If m is the calculated quantity, x_i the measured values and Δx_i the uncertainty of each value, the total uncertainty is
Δm = ∑ | dm / dx_i | Dx_i
for instance:
If the magnitude is a average of two magnitudes measured each with a different error
m =
Δm = | | Δx₁ + |
| Δx₂
= ½
= ½
Δm = Δx₁ + ½ Δx₂
Δm = Δx₁ + Δx₂
In conclusion, using the propagation errors we can find the uncertainty of a given quantity is the sum of the uncertainties of each measured quantity.
Learn more about propagation errors here:
The magnetic force (Lorentz force) experienced by the proton in the magnetic field is given by
since
, because the velocity v and the force F in this problem are perpendicular, and so also the angle 
between the velocity and the magnetic field B should be 
.
Let's find the magnitude of the magnetic field; this is given by
To understand the direction, let's use the right-hand rule:
-index finger: velocity
- middle finger: magnetic field
- thumb: force
Since the velocity (index) points east and the force (thumb) points south, then the magnetic field (middle finger) points downwards. So we write:
B = -0.091 T
since
Let's find the magnitude of the magnetic field; this is given by
To understand the direction, let's use the right-hand rule:
-index finger: velocity
- middle finger: magnetic field
- thumb: force
Since the velocity (index) points east and the force (thumb) points south, then the magnetic field (middle finger) points downwards. So we write:
B = -0.091 T