You just built a new apparatus. Inside the apparatus, an electron travels horizo

Question

You just built a new apparatus. Inside the apparatus, an electron travels horizontally through a vertical uniform electric field with the velocity v = <1750, 0, 0> m/s. Without the electric field, the electron would fall down due to the gravitational force. What is the electric field inside the apparatus? (First draw a picture.) Represent your answer as a vector in the form E=(Ex,Ey,Ez).
Provide the answer by filling in the blanks below:
<________, ____________ , ___________ > N/C

Please help ASAP, thank you in advance

Explanation / Answer

Since you have not specified, I assume the coordinate frame is oriented in such a way that the X and Y-axes are in the plane of the ground, and the Z- axis is the height above ground.
With this reference frame, the electron is traveling with a velocity of (1750,0,0)m/s. Since it has a constant velocity, there must be no net force acting on it. The only forces acting on the electron are gravity and the force due to the electric field. These two forces must balance out each other so that the net force acting on it is zero.
mg = Ee where e is the charge on an electron.

(9.1 * E-31 kg) * 9.8 m/s2 = E * (-1.6 * E-19 C)

which gives E = 5.574 * E-11 N/C

Since gravity is acting downwards, we want the electrostatic force on the electron to be acting upwards, So the electric field must be acting in the same direction as gravity (recall that the charge on the electron is negative!)

Answer: <0, 0, -5.574 * E-11> N/C

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