An accelerating voltage of 2.46 * 10^3 V is applied to an electron gun, producing a beam of electrons originally traveling horizontally north in vacuum toward the center of a viewing screen 34.0 cm away.

What is the magnitude of the deflection on the screen caused by the Earth's gravitational field?

I am using this formula
v = squareroot(-2*q*V/m) to find speed and then B = mv/er for the magnitude

but they are asking the answer to be in meters...

Well, I have a problem with the second equation. The deflection of the particle traveling in a magnetic field is based on force

Force=m v B SinTheta where Theta is the angle between velocity and B.
http://www.ux1.eiu.edu/~cfadd/1360/29MagFlds/HmwkSol.html

But here, the velocity is North, which is almost parallel with the Earth's magnetic field, or zero force, and no deflection.
Now in reality, The Earths magnetic field is not exactly North, and depending with latitude, not exactly parallel with Earth's axis. So it is somewhat complicated the exact angle between v and North Magnetic.
I suspect you teacher wants you to assume zero force.

sir i read through the site so when i use force 0 how should i solve this question?

thank you

To find the magnitude of the deflection caused by the Earth's gravitational field, we need to consider the effect of both the electric field produced by the accelerating voltage and the magnetic field produced by Earth's gravitational field.

First, let's calculate the speed of the electrons using the given voltage. The formula you mentioned, v = √(-2*q*V/m), is correct, where q is the charge of an electron, V is the voltage, and m is the mass of an electron.

For an electron, q = -1.6 x 10^-19 C and m = 9.11 x 10^-31 kg. Plugging in these values along with the voltage V = 2.46 x 10^3 V, we can calculate the speed (v) of the electrons.

v = √(-2 * -1.6 x 10^-19 C * 2.46 x 10^3 V / 9.11 x 10^-31 kg)

Calculating this equation will give you the speed of the electrons.

Now, let's find the magnitude of the magnetic field (B) caused by Earth's gravitational field. Given that the distance (r) from the electron source to the center of the screen is 34.0 cm (or 0.34 m) and the speed (v) of the electrons, we can use the formula B = mv/(er) to calculate the magnitude of the magnetic field.

Plugging in the values:

B = (9.11 x 10^-31 kg * v) / (0.34 m * (1.6 x 10^-19 C))

Calculating this equation will give you the magnitude of the deflection caused by the Earth's gravitational field.

However, please note that the given formula assumes a constant magnetic field throughout the path of the electrons, which might not be the case in this scenario.

see my answer posted elsewhere