A proton moves through a region containing a uniform electric field given by = 81.0 ĵ V/m and a uniform magnetic field

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A proton moves through a region containing a uniform electric
field given by = 81.0 ĵ V/m and
a uniform magnetic field = (0.200 î + 0.300 ĵ + 0.400 ) T.
Determine the acceleration of the proton when it has a
velocity = 151 î m/s.
Step 1
The electric field in this problem is weak, the magnetic field
is strong, and the velocity of the proton is small for a proton, on
the order of a few hundred meters per second. Both fields
contribute to the net force on the proton. This force is on the
order of a fraction of a newton and will cause an acceleration of
large magnitude. The acceleration due to gravity is negligible.
Step 2
We will use the Lorentz force equation, which computes the
vector addition of the forces on the particle. We will use Newton's
second law with the particle under net force model.
Step 3
Applying Newton's second law and the Lorentz force law, we
have
= m = q + q × .Solving
for the acceleration gives =
+ ×
,where e is the charge
and m is the mass of the proton. For
× ,
we have the following determinant in which we have
suppressed the SI units for this step.

A Proton Moves Through A Region Containing A Uniform Electric Field Given By 81 0 J V M And A Uniform Magnetic Field 1 (43.02 KiB) Viewed 25 times

196 à = e E + VB m X where e is the charge and m is the mass of the proton. For ū B, we have the following determinant in which we have suppressed the SI units for this step. î j K 151 0.16*10**-17 X 0.2 0.3 0.3 0.4 0 0 -60.4 0.2 0.4 + The response you submitted has the wrong sign. ſ + 1.008*10**-17 X 45.3 Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. Step 4 For the vector sum Ę + y +B , we have the following result with SI units suppressed. ē = 45.3 x 20.6 + B Your response differs from the correct answer by more than 100%. + 45.3 45.3 Step 5 Finally, for the acceleration of the proton, we have the following. à = e E + B X m 1.60 x 10-19 1.67 * 10-27 i + ਸੀ । N/C kg j + K] * 10° m/s2 K Submit Skip (you cannot come back) Need Heln2 Pond It