Use the worked example above to help you solve this problem. A proton moves with

Question

Use the worked example above to help you solve this problem. A proton moves with a speed of 1.16 Times 10^5 m/s through Earth's magnetic field, which has a value of 58.1 mu T at a particular location. When the proton moves eastward, the magnetic force acting on it is directed straight upward, and when it moves northward, no magnetic force acts on it. What is the direction of the magnetic field? What is the strength of the magnetic force when the proton moves eastward? Calculate the gravitational force on the proton and compare it with the magnetic force. Compare it also with the electric force if there were an electric field with magnitude E = 1.50 Times 10^2 N/C at that location, a common value at Earth's surface. Note that the mass of the proton is 1.67 Times 10^-27 kg. Suppose an electron is moving due west in the same magnetic field as in the example at a speed of 2.60 Times 10^5 m/s. Find the magnitude and direction of the magnetic force on the electron.

Explanation / Answer

Here ,

speed of proton , u = 1.16 *10^5 m/s

magnetic field , B = 58.1 uT

a)

as magnetic force = q * V X B

as there is no force when the proton moves in north direction

the direction of magnetic field is north

b)

force= q * V * B

force = 1.602 *10^-19 * 1.16 *10^5 * 58.1 *10^-6

force = 1.08 *10^-18 N

the strength of magnetic force when the proton is 1.08 *10^-18 N

c)

Fgrav = m * g

Fgrav = 1.67 *10^-27 * 9.8

Fgrav = 1.64 *10^-26 N

Fele = 1.5 *10^2 * e

Fele = 2.403 *10^-17 N

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