Acceleration of a Charged Particle

[rum2563]

Homework Statement

A positively charged particle of mass 3.0 X 10 ^-12 kg and charge +6.4 X 10^-5 C is perpendicular to a 1.5 T magnetic field. If the particle has a speed of 4.8 X 10^3 m/s, the acceleration of the particle...?

Homework Equations

e = kg / r^2
qB = mv / r

The Attempt at a Solution

Given information:
m = 3.0 X 10 ^-12 kg
q = 6.4 X 10^-5 C
B = 1.5 T
v = 4.8 X 10^3 m/s

To find the acceleration, I started reading my book, and I found the equation:
q = mg / e
So if I rewrite this to find "g", it should be like this:
g = qe / m


BUT, I don't know e, so to find e (epsilon), I must first know the radius "r"
r = mv / qB
= (3.0 X 10 ^-12)(4.8 X 10^3) / (6.4 X 10^-5)(1.5)
= 1.5 X 10 ^-4 m

Now, I can find e:
e = kq / r^2
= (9 X 10^9)(6.4 X 10^-5) / (1.5 X 10^-4)^2
= 2.56 X 10^13 N/C

Now, I can find "g"

g = qe / m
= (6.4 X 10^-5)(2.56 X 10^13) / (3.0 X 10 ^-12)
= 5.46 X 10^20 m/s^2

But this is not the correct answer.

The correct answer should be one of the following:
3.4 X 10^-4
2.6 X 10^-20
1.5 X 10^11
1.5 X 10^-4
1.7 X 10^19

Someone please help me. I think there should be another way to do this. Please help me. Thank you.

 

[G01]

The relationships you are using are not correct in this case. The first one is the definition of an electric field (e stands for the electric field). The second is incorrect. "qB" is not a useful quantity. I think the relationship you were thinking of was qE=mv^2/r, which describes circular motion with the electric force as the centripetal force. Either way, it doesn't apply to this problem.

I think the best way to solve this would be to go back to fundamentals. Remember Newton's Second Law:

$$\Sigma F = ma$$

You want the find a, you know the mass, m, and the force here is the magnetic force. HINT: Do you know a relationship to find the magnetic force on a particle moving through a constant magnetic field?

I hope this helped. If you need more help, I'll answer as soon as I can.
Good Luck!

 

[m2003]

I can confirm that your approach to finding the acceleration is correct. However, it seems that there may be an error in your calculations. When finding the radius, the correct calculation should be r = mv / qB = (3.0 X 10 ^-12)(4.8 X 10^3) / (6.4 X 10^-5)(1.5) = 1.5 X 10^-4 m. This small error in the radius may have led to the incorrect value for the acceleration. I suggest redoing the calculations with the correct radius and see if you get the correct answer. Additionally, it may be helpful to check and double check your calculations to ensure accuracy.