Amicrowave oven operates with sinusoidal microwaves at a frequency of 2400 mhz. the height of the oven cavity is 25 cm and the base measures 30 cm by 30 cm. assume that microwave energy is generated uniformly on the upper surface of the cavity and propagates directly downward toward the base. the base is lined with a material that completely absorbs microwave energy. the total microwave energy content of the cavity is 0.50 µj. what magnitude force does the microwave beam exert on the base of the oven?

Explanation:

From the problem we have

Where is frequency, is height, and is the microwave energy.

First of all, we need to tranform length units to meters. In the case of the heigh, we just have to divide by 100, because 1 meter equals 100 centimeters:

Then, the area of the base would be

Now, to find the force exterted on the base of the oven, we first need to find the radiation pressure. But, before that, we need to know the intensity, and to find it, we need to first calculate the power, which is defined as

Where is the power, is the energy and is the time.

Replacing all values, we have

As you can see, we need to find the time of the movement of the microwave beam, wich is can be found using constant kinematics

where is the speed of the light (we are talking about an electromagentic wave), is the height (the distance that the beam will travel), and is the time of the movement.

Also, we know that

Replacing all values, we find the time

Now, we can find the power

Then, we calculate the intensity

Now, the radiation pressure

Lastly, using this radiation pressure we can find the force that cause it

Therefore, the force exterted on the base of the oven is