A particle (mass = 4.0 g, charge = 80 mC) moves in a region of space where the electric field is uniform and is given by Ex = -2.5 N/C, Ey = Ez = 0. If the velocity of the particle at t = 0 is given by vx = 80 m/s, vy = vz = 0, what is the speed of the particle at t = 2.0 s?

Answer :

skyluke89

Answer:

20 m/s

Explanation:

The force experienced by a charged particle in an electric field is given by

[tex]F=qE[/tex]

where, in this problem:

[tex]q=80 mC=0.080 C[/tex] is the charge of the particle

E is the electric field

The electric field here has components:

[tex]E_x=-2.5 N/C\\E_y=0\\E_z=0[/tex]

So the components of the force experienced by the particle are:

[tex]F_x=qE_x=(0.080)(-2.5)=-0.2 N\\F_y=0\\F_z=0[/tex]

Now we can find the components of the acceleration experienced by the particle, using Newton's second law of motion:

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

where

m = 4.0 g = 0.004 kg is the mass of the particle

The 3 components of the acceleration are:

[tex]a_x=\frac{F_x}{m}=\frac{-0.2}{0.004}=-50 m/s^2\\a_y=0\\a_z=0[/tex]

Now we can find the components of the velocity of the particle at time t using the suvat equation:

[tex]v=u+at[/tex]

where:

[tex]u_x=80 m/s\\u_y=0\\u_z=0[/tex]

are the initial components of the velocity

Therefore, at t = 2.0 s, we have:

[tex]v_x=u_x+a_xt=80+(-50)(2.0)=-20 m/s\\v_y=u_y+a_yt=0+0=0\\v_z=u_z+a_zt=0+0=0[/tex]

And so, the speed of the particle is the magnitude of the final velocity:

[tex]v=\sqrt{v_x^2+v_y^2+v_z^2}=\sqrt{(-20)^2+0+0}=20 m/s[/tex]

Cricetus

The speed of particle at t = 2.0 s would be:

20 m/s

Electric field

According to the question,

Mass, m = 4.0 g

Charge, q = 80 mC

Uniform electric field, Ex = -2.5 N/C

Velocity, [tex]v_x[/tex] = 80 m/s

               [tex]v_y[/tex] = [tex]v_z[/tex] = 0

Time, t = 2.0 s        

Now,

The force on the particle will be:

→ F = qE

By substituting the values,

     = 0.080 × -2.5

     = -0.200 Newtons

then,

→ a = [tex]\frac{F}{m}[/tex]

      = [tex]-\frac{0.200}{0.004}[/tex]

      = -50 m/s²

hence,

The final speed be:

= Initial speed + at

= 80 + (-50) × 2.0

= -20 m/s

Thus the above answer is correct.

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