Proton hits infinite charged plane, find charge of plane

[aliaze1]

Homework Statement

An electron is released from rest 2.0 cm from an infinite charged plane. It accelerates toward the plane and collides with a speed of 1*10⁷ m/s

What is the surface charge density of the plane?

Homework Equations

a=(qE)/m
v=v₀+a∆t

The Attempt at a Solution

v₀=0
therefore a∆t = 1*10⁷ m/s
∆t=L/v₀

calculating the time ∆t requires knowledge of either v₀ or a, v₀ is zero, so one cannot calculate it using v₀, so the other option is to use a, which is unknown also

How would I go about this?

Once I have a, i can find E using the formula a=(qE)/m

Thanks

 

[mishraanwesh]

The electric field intensity of an infinite charged plate is given by-

E=S/2E0

E0=8.854*10 powered to -12 S is the surface charge density.

substitue the above formula as the E for the the a=(qE)/m then proceed as planned.

report if your work was done

 

[baba89]

for your question. To find the charge of the plane, we first need to determine the acceleration of the electron towards the plane. We can use the equation a=(qE)/m, where a is the acceleration, q is the charge of the electron, E is the electric field, and m is the mass of the electron.

Since the electron is released from rest, its initial velocity (v0) is zero, so we can use the equation v=v0+at to solve for the time (t) it takes for the electron to collide with the plane. We know the final velocity (v) is 1*107 m/s, so we can rearrange the equation to solve for t:

t=(v-v0)/a= (1*107 m/s - 0 m/s)/(qE/m) = (1*107*m*s^2)/(qE)

Now, we can use this value of t to solve for E using the equation E=ma/q. We know the mass of an electron (m) and the acceleration (a) from the previous equations, so we can plug those values in and solve for E:

E=(ma)/q= ((9.11*10^-31 kg)*(1*107 m/s^2))/ (-1.6*10^-19 C) = -5.69*10^11 N/C

Since we know the electric field, we can now use the equation E=σ/ε0 to solve for the surface charge density (σ) of the plane. ε0 is the permittivity of free space and has a value of 8.85*10^-12 C^2/N*m^2. Plugging in our values, we get:

σ=(E*ε0) = (-5.69*10^11 N/C)*(8.85*10^-12 C^2/N*m^2) = -5.03*10^-2 C/m^2

Therefore, the surface charge density of the plane is -5.03*10^-2 C/m^2.

Hope this helps!