Two parallel, metal plates with separation distance d = 1.00 cm carry charges of equal magnitude but opposite sign. The plates are oriented horizontally. Assume the electric field between the plates is uniform, and it has a magnitude of 1,920 N/C. A charged particle with mass 2.00 â 10^â16 kg and charge 1.02 â 10%â6 C is projected from the center of the bottom negative plate with an initial speed of 1.07 â 10%5 m/s at an angle of 37.0° above the horizontal. Assume the plates are square with side length = 20.0 cm.

Required:
a. Describe the trajectory of the particle.
b. Which plate does it strike?
c. Where does it strike, relative to its starting point?
d. What is the minimum initial speed (in m/s) the particle must have in order to change the answer to part (b)?

Respuesta :

Answer:

g

Explanation:

We have that  the trajectory of the particle,The plate the particle strikes,Where it strikes, relative to its starting point and the minimum initial speed (in m/s) the particle must have in order to change the answer to part (b) are as follows

  • Parabola
  • Negative plate
  • [tex]a=9.792x10^{12}m/s^2[/tex]
  • [tex]V_m=570452.106m/s[/tex]

From the question we have that

Distance [tex]d=1.00cm=0.01m[/tex]

Magnitude  [tex]M=1,920 N/C[/tex]

Mass [tex]m=2.00x10^{-16} kg[/tex]

Charge [tex]q=1.02x10^{-6} C[/tex]

initial speed [tex]V_0= 1.07x10^5 m/s[/tex]

Angle [tex]\theta= 37[/tex]

Length [tex]l= 20.0 cm.[/tex]

a)

The Particle follow a Parabola trajectory through its travel as a Parabola Creates a Curved Plane and has its initial half side same as the final side.with the particle is a [tex]\theta= 37[/tex] angle create on its elevation and depression

Parabola

b)

It strikes the Negative plate at a specific distance to be discovered in the C part of the Question

c)

We are tasked to determine where the particle strikes the plate.

Generally the equation for strike distance S  is mathematically given as

[tex]s=\frac{v_0^2 sin(2\theta)}{a}[/tex]

Where

[tex]a=\frac{qM}{m}[/tex]

[tex]a=\frac{1.02x10^{-6}x1920}{2.00x10^{-16} }[/tex]

[tex]a=9.792x10^{12}m/s^2[/tex]

Therefore

[tex]s=\frac{v_0^2 sin(2\theta)}{a}[/tex]

[tex]\frac{(1.07x10^5)^2 xsin(2*37)}{9.792x10^{12}}[/tex]

[tex]s=0.0011239m[/tex]

d)

Generally the equation for  the minimum Velocity  is mathematically given as

[tex]V_m=\sqrt{\frac{2ah}{sin(\theta)}}[/tex]

[tex]V_m=\sqrt{\frac{2x9.792*10^{12}*0.01}{sin(37)}}[/tex]

[tex]V_m=570452.106m/s[/tex]

In conclusion

The trajectory of the particle,The plate the particle strikes,Where it strikes, relative to its starting point and the minimum initial speed (in m/s) the particle must have in order to change the answer to part (b) are as follows

  • Parabola
  • Negative plate
  • [tex]a=9.792x10^{12}m/s^2[/tex]
  • [tex]V_m=570452.106m/s[/tex]

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