Instruction

1

For example, you need to solve this problem. The electron moves in a uniform magnetic field with the induction value In describing a perfectly circular trajectory. It acts the Lorentz force Fл. The centripetal acceleration

**of the electron**is equal to "a". You want to calculate**the speed**of motion**of the electron**.2

For starters, let's remember what the Lorentz force and how it is calculated. It is the force with which the electromagnetic field acts on a single charged particle. In your case, the conditions of the problem (the electron is in a magnetic field moves in a circle of constant radius), the Lorentz force will be the centripetal force and calculated according to the following formula: Fл = еvB. Value Fл and given to you under the terms of the task, the amount of charge

**of the electron**e is easily found in any reference book.3

On the other hand, the Lorentz force (like any force) can be expressed by the following formula: Fл = ma. The mass

**of the electron**m are also easily located with the help of reference books.4

Equating these expressions, you will see that evB is equal to ma. The only unknown you value the same

**speed**v, and that it is necessary to find. By elementary transformations, you get: V = ma/eB. Substituting in the formula the values (as data for the problem and found your own), you will receive a response.5

Well, what about, for example, if you know neither the magnitude of induction or Lorentz force Fл, and instead is given only the radius of the circle r, which rotates the same electron? In this case, to determine its

**speed**? Recall the formula for centripetal acceleration: a = v2/r. Hence: v2 = ar. After removing the square root from the product of magnitudes of the centripetal acceleration and the radius of the circle you get the desired**speed****of the electron**.# Advice 2 : How to find the centripetal acceleration

Centripetal acceleration appears when a body moves in a circle. It is directed to its center, measured in m/S2. A feature of this type of acceleration is that it is, even when the body is moving with constant speed. It depends on the radius of the circle and the linear velocity of the body.

You will need

- speedometer;
- - instrument for measuring distances;
- - stopwatch.

Instruction

1

To find the centripetal acceleration, measure the velocity of a body moving along a circular trajectory. You can do this using a speedometer. If you install this device is not possible, calculate the linear speed. To do this, note the time that it took for a full rotation on a circular path.

2

It is the period of rotation. Let's Express it in seconds. Measure the radius of the circle on which the moving body with a ruler, measuring tape or a laser rangefinder in meters. To find the speed find the product of the number 2 to the number π≈3.14, and the radius R of the circle and divide the result by the period T. This will be linear velocity of the body v=2∙π∙R/T.

3

Find the centripetal acceleration AC by dividing the square of the linear velocity v on the radius of the circle on which the moving body is R (AC=v2/R). Using formulas to determine the angular velocity, frequency and period of rotation, find that value in other formulas.

4

If you know the angular velocity ω and the radius of the trajectory (the circle in which the body moves) R the centripetal acceleration will be equal to AC= ω2∙R. When you know the period of rotation of the body T, and the radius of the trajectory R, then AC= 4∙π2∙R/T2. If we know the speed ν (the number of complete rotations per second), determine the centripetal acceleration by the formula AC= 4∙π2∙R∙ν2.

5

Example: the car, the radius of the wheels of which 20 cm is moving down the road at a speed of 72 km/h. Determine the centripetal acceleration of the extreme points of the wheels.

Solution: the linear velocity of points of any wheel is 72 km/h=20 m/s. wheel Radius in meters R=0.2 m. Calculate the centripetal acceleration substituting the resulting numbers into the formula AC=v2/R. Get ATS=202/0,2=2000 m/S2. This centripetal acceleration under uniform rectilinear motion will be at the extreme points of all four wheels of the car.

Solution: the linear velocity of points of any wheel is 72 km/h=20 m/s. wheel Radius in meters R=0.2 m. Calculate the centripetal acceleration substituting the resulting numbers into the formula AC=v2/R. Get ATS=202/0,2=2000 m/S2. This centripetal acceleration under uniform rectilinear motion will be at the extreme points of all four wheels of the car.