(Help) Surface charge density (σ) for particle to hit plate...

AI Thread Summary
The discussion revolves around calculating the surface charge density (σ) for a particle impacting a plate. The initial calculations involve using projectile motion equations and electric field formulas, but the user encounters difficulties due to having two unknowns. Suggestions are made to find acceleration using kinematics instead, emphasizing the importance of incorporating units in calculations. Additionally, the conversation touches on the use of SUVAT equations for projectile motion and the expression for range when a projectile returns to its launch level. The thread highlights the need for clarity in the approach to solving the problem.
chrisbroward
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Homework Statement
Find surface charge density required for t = 11.4 ms (11.4 * 10^-3 s)

Answer in μC/m^2
Relevant Equations
q = -3.84 mC (-3.84 * 10^-3 C)
m = 3.38 g
ⱴ = 6.81 km/s (6810 m/s)
θ = 69.1°
all at t = 0.
SCR-20240131-mzrk.png


I don't know if i'm exactly right.

But I started with x(time) = V cos θ t
which = (6810 m/s) cos (69.1°) (11.4 * 10^-3 s)
is ... 27.69 m

& since Electric field due to uniformly charge surface is represented by...
E = (q * σ)/(2 * ε_0 * m), and since acceleration (a) can be expressed as F/m, and Force (F) can be express as q*E;
I can combine these two equations...

a must be = (-3.84 * 10^-3 * σ)/(2 * (8.85 * 10^-12) * (3.38 * 10^-3)),
which is -6.418 * 10^10 * σ = a.

But as you can see now I have two unknowns and can't solve :(

Can anyone outline what exactly i'm doing incorrectly?
 
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You would want to find acceleration another way. Since you know t/2 and can find the velocity in the y-direction, you can use kinematics to find the acceleration.
 
Apart from the above: Please use units.
 
Are you used to using the SUVAT equations in ballistics questions?
 
Or knowing ##v_x## and the time of flight you can find the range. What is an expression for the range for a projectile that returns to the same level from which it was launched?
 
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