- #1
prslook26
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Homework Statement
The drawing shows a particle carrying a positive charge +q at the origin (of x and y axis), as well as a target location located in the lower left quadrant. The target is just as far from the x-axis as it is from the y axis. There is also a uniform magnetic field directed away from you. Our goal is to start the charge moving in the correct direction, and with the correct speed, so that the magnetic force on the charge will cause it to hit the target.
(a) In which direction(s) could the charge begin moving and, assuming the correct speed, reach the target location? You have four choices for the direction: +x, -x, +y, or -y. Note that more than one answer may be correct. Explain your reasoning.
(b) Assign any values you like for the magnetic field strength B (in Tesla), the charge q (in Coulombs), and the coordinates of the target point (in meters).
What must the speed of the charge be in order to reach the target location? Give your answer in m/s. (Note that your answer will be the same no matter which answer you gave in part (a) above, provided you answered part (a) correctly.)
Homework Equations
The Attempt at a Solution
(a) I apologize for not being able to provide a graph for this problem, I couldn't find it anywhere online.
So, since the charge is positively charged, it will start moving counterclockwise in the uniform magnetic field, which will be in the negative direction for both x and y-axis - in other words towards the target, which is in the lower left quadrant. But since I wasn't given exact coordinates of the target, can I simply assign my own numbers (say: -3,-3) for the target and say that the charge needs to move -3 on the x-axis and -3 on the y-axis in order to reach the target?
I feel like this sounds too simple to be correct!
(b) In order to find the speed of the charge, we assume that the magnetic force equals its centripetal force:
Fm = Fc
qV1B = m x V1^2/r
V1 = rqB/m
If target is at (-3,-3), then it's really a square, so the radius is simply:
a^2+b^2=c^2
c=4.24 m (square root of 18)
Let's also assume:
+q = 1.60x10^-19 C
m = 1.67x10^-27 kg
B = 4x10^-4 T
Solving for speed:
V = [(4.24m)(1.60x10^-19 C)(4x10^-4 T)] / 1.67x10^-27 kg
V = 1.62 x 10^5 m/s
Am I even close with this? I have been staring at this problem for hours and this is all that I'm coming up with. Help!
Thank you in advance!