How Do Weight and Magnetic Force on an Electron Compare Near Earth's Surface?

[kidia]

How can I Compare the magnitudes near the earth’s surface of the weight of an electron and a typical magnetic force exerted by the earth’s magnetic field (B = 10-5T) on an electron with speed 10 m/s.

As I understood Weight of electron = mg
Magnetic force=qBv

am I right?

 

[Doc Al]

Sounds good to me. (Note that magnetic force = qvB assumes that the electron's velocity is perpendicular to the magnetic field.)

 

[kyle8921]

Yes, you are correct. The weight of an electron can be calculated as mg, where m is the mass of the electron and g is the acceleration due to gravity near the Earth's surface. On the other hand, the magnetic force exerted on the electron by Earth's magnetic field can be calculated as qBv, where q is the charge of the electron, B is the strength of the magnetic field, and v is the velocity of the electron.

To compare the magnitudes of these two forces, we can plug in the values for each variable. The mass of an electron is approximately 9.11 x 10^-31 kg, and the acceleration due to gravity near Earth's surface is approximately 9.8 m/s^2. This gives us a weight of approximately 8.92 x 10^-30 N.

For the magnetic force, we can use the given values of B = 10^-5 T and v = 10 m/s. The charge of an electron is approximately 1.6 x 10^-19 C. Plugging these values into the equation, we get a magnetic force of approximately 1.6 x 10^-23 N.

Comparing these two values, we can see that the magnetic force is significantly smaller than the weight of the electron. This is because the magnetic force is dependent on the velocity of the electron, which is much smaller than the acceleration due to gravity near Earth's surface. Therefore, the weight of the electron is much larger compared to the magnetic force exerted on it by Earth's magnetic field.