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 not getting what we have to find here...
thank you
Under the influence of g, the electron drops slightly on the way to the screen. Calculate by how much.
You need to first get the speed V of the electron (using the beam voltage) and, from that, the time it takes to reach the screen. Call that time t
t = 0.34 m/V
The gravitational deflection of the electron beam is (g/2)*t^2
To find the magnitude of the deflection on the screen caused by the Earth's gravitational field, we first need to understand the effect of the Earth's gravitational field on the electrons. Since the electrons are traveling horizontally north, the gravitational force will act vertically downwards. This force will cause the electrons to deflect as they move towards the screen.
We can calculate the deflection using the laws of motion and basic principles of physics. Here are the steps to find the magnitude of the deflection:
1. Determine the time it takes for the electrons to reach the screen:
The distance to the screen is given as 34.0 cm. Since the electrons are initially traveling horizontally north, this distance is the horizontal component of the total distance traveled by the electrons. We can use the average speed formula: distance = speed × time. Rearranging the formula, we have time = distance / speed.
Here, speed refers to the initial horizontal speed of the electrons, which is not given directly but can be determined using the accelerating voltage applied to the electron gun.
2. Calculate the initial horizontal speed of the electrons:
The accelerating voltage applied to the electron gun can be used to determine the kinetic energy of the electrons. Since the electrons are negatively charged, the accelerating voltage will increase their kinetic energy. The kinetic energy is given by the formula: KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass of an electron, and v is its speed. Rearranging the formula, we have v = √(2KE / m), where m can be obtained from the known mass of an electron.
3. Determine the vertical displacement of the electrons due to the gravitational force:
The vertical displacement can be calculated using the formula: displacement = (1/2)gt^2, where g is the acceleration due to gravity and t is the time calculated in step 1.
4. Calculate the magnitude of the deflection on the screen:
The magnitude of the deflection is the vertical displacement determined in step 3.
By following these steps and plugging in the given values, you can find the magnitude of the deflection on the screen caused by the Earth's gravitational field.