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

In summary, the surface charge density (σ) is a crucial parameter in determining whether a charged particle will successfully hit a plate. It influences the electric field around the plate, which in turn affects the motion of the particle. Calculating the appropriate σ allows for the prediction of the conditions under which the particle can overcome repulsive forces and make contact with the plate.
  • #1
chrisbroward
9
1
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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  • #2
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.
 
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  • #3
Apart from the above: Please use units.
 
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  • #4
Are you used to using the SUVAT equations in ballistics questions?
 
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  • #5
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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FAQ: (Help) Surface charge density (σ) for particle to hit plate...

```html

What is surface charge density (σ) and how is it defined?

Surface charge density (σ) is defined as the amount of electric charge per unit area on a surface. It is measured in coulombs per square meter (C/m²). Mathematically, it is given by σ = Q/A, where Q is the total charge and A is the area over which the charge is distributed.

How does surface charge density (σ) affect the motion of a particle towards a plate?

The surface charge density (σ) creates an electric field around the plate. This electric field exerts a force on charged particles, influencing their motion. A higher surface charge density results in a stronger electric field, which can either attract or repel a particle depending on the sign of its charge.

What is the relationship between surface charge density (σ) and the electric field (E) near a charged plate?

The electric field (E) near a charged plate is directly proportional to the surface charge density (σ). For an infinite plane of charge, the electric field can be calculated using the formula E = σ / (2ε₀), where ε₀ is the permittivity of free space. This relationship assumes the plate is uniformly charged and the field is being measured close to the surface.

How can we calculate the minimum surface charge density (σ) required for a particle to hit a plate?

To calculate the minimum surface charge density (σ) required for a particle to hit a plate, you need to consider the forces acting on the particle, including the electric force due to the plate's charge and any other forces such as gravitational or initial kinetic energy. By setting up the equations of motion and solving for σ, you can determine the minimum value needed for the particle to reach the plate.

What experimental methods can be used to measure surface charge density (σ) on a plate?

Surface charge density (σ) can be measured using several experimental methods, including the use of an electrometer to measure the charge directly, or by using a field mill to measure the electric field and then calculating σ from the field strength. Another method involves using a Faraday cup to collect the charge and then determining the surface charge density from the collected charge and the area of the plate.

```

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