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 vertical component of the Earth's magnetic field, taken as 20.0 µT down?

thank you

Force=Bqv, so covert the accelerating voltge to velocity (by kinetic energy).

1/2 m v^2=Voltage*e

solve for v, then force=Bq*velocity

Now, having the deflecting force, find the time to the screen (time=.34/velocity) which is the time in the deflecting force, so finally,
deflection= 1/2 (force/masselectgron)t^2

check all that.

oh alright sir thank you!

To find the magnitude of the deflection caused by the vertical component of the Earth's magnetic field on the screen, we need to calculate the magnitude of the magnetic force acting on the electrons.

The formula for the magnitude of the magnetic force (F) on a moving charged particle is:

F = qvB

Where:
- q is the charge of the particle
- v is the velocity of the particle
- B is the magnetic field strength

In this case, the charged particle is an electron (with a charge of -1.6 x 10^-19 C), the velocity of the particle is the initial velocity of the electrons produced by the electron gun (which is horizontal north in this case), and the magnetic field strength is given as 20.0 µT (or 20.0 x 10^-6 T).

To find the magnitude of the deflection, we need to calculate the horizontal component of the velocity (v_h) and the vertical component of the velocity (v_v) of the electrons.

Given that the initial velocity of the electrons is horizontal north, we can split the velocity into its horizontal and vertical components as follows:

v_h = v
v_v = 0

Now, we can substitute the values into the formula for the magnitude of the magnetic force:

F = qvB

F = (-1.6 x 10^-19 C)(v)(20.0 x 10^-6 T)

Since the formula for acceleration (a) is given by:

F = ma

We can rearrange the formula to solve for acceleration:

a = F/m

Where:
- m is the mass of the electron

The mass of an electron (m) is approximately 9.11 x 10^-31 kg.

Now, we can substitute the values into the formula for acceleration:

a = (-1.6 x 10^-19 C)(v)(20.0 x 10^-6 T) / (9.11 x 10^-31 kg)

The acceleration (a) represents the change in velocity over time. In this case, the electrons are traveling horizontally and will continue to do so, so the vertical component of the force will not change the horizontal velocity of the electrons.

Hence, the magnitude of the deflection on the screen caused by the vertical component of the Earth's magnetic field is zero.

To determine the magnitude of the deflection on the screen caused by the vertical component of the Earth's magnetic field, we need to use the principles of the Lorentz force and the equation for the deflection of a charged particle in a magnetic field.

The Lorentz force is given by the equation:

F = q(v x B)

where F is the force experienced by the charged particle, q is the charge of the particle, v is the velocity vector of the particle, and B is the magnetic field vector.

In this case, we have an electron beam, so the charge of the electron is q = -1.6 * 10^-19 C.

To determine the velocity of the electrons, we can use the given information that they are originally traveling horizontally north. Since no other information about the speed is provided, we assume a typical speed for electrons of approximately 10^7 m/s.

The given vertical component of the Earth's magnetic field is -20.0 µT (downward). To convert this to tesla, we divide by 10^6:

B = -20.0 µT = -20.0 * 10^-6 T

Now, we can plug these values into the Lorentz force equation:

F = q(v x B)
= (-1.6 * 10^-19 C)(10^7 m/s)(-20.0 * 10^-6 T)

The force will determine the deflection of the electrons on the screen. To calculate the deflection, we need to know the length of time the electrons are exposed to the Earth's magnetic field. The question does not provide this information, so we cannot calculate the exact deflection.

However, we can calculate the maximum deflection angle by assuming the electrons are deflected 90 degrees before reaching the screen. This means the force is acting on the electrons for a time interval of t = L/v, where L is the distance to the screen (34.0 cm), and v is the velocity of the electrons (10^7 m/s).

t = L/v = (34.0 cm)(1 m/100 cm)/(10^7 m/s)
= 3.4 * 10^-7 s

Now, let's calculate the maximum deflection angle (θ) using the time interval and the force calculated previously:

F = ma = q(v x B) = mv^2/r = qvB => qvB = ma
=> a = (qvB/m) = (q/m)(vB)
=> θ = (1/2)*a*t^2 = (1/2)(q/m)(vB)(t^2)
= (1/2)(-1.6 * 10^-19 C / 9.11 * 10^-31 kg) * (10^7 m/s) * (-20.0 * 10^-6 T) * (3.4 * 10^-7 s)^2

After calculating this, you should get the magnitude of the deflection on the screen caused by the vertical component of the Earth's magnetic field.