(a) Determine the transmission power P of your cell phone....

(a) Determine the transmission power $P$ of your cell phone. (This information is available online.) (b) A typical cell phone battery supplies a $1.5 \mathrm{~V}$ potential. If your phone battery supplies the power $P,$ what is a good estimate of the current supplied by the battery? (c) Estimate the width of your head. (d) Estimate the diameter of the phone speaker that goes next to your ear. Model the current in the speaker as a current loop with the same diameter as the speaker. Use these values to estimate the magnetic field generated by your phone midway between the ears when it is held near one ear. (e) How does your answer compare to the earth's field, which is about $50 \mu \mathrm{T} ?$

(a) Determine the transmission power $P$ of your cell phone. (This information is available online.) (b) A typical cell phone battery supplies a $1.5 \mathrm{~V}$ potential. If your phone battery supplies the power $P,$ what is a good estimate of the current supplied by the battery?
(c) Estimate the width of your head.
(d) Estimate the diameter of the phone speaker that goes next to your ear. Model the current in the speaker as a current loop with the same diameter as the speaker. Use these values to estimate the magnetic field generated by your phone midway between the ears when it is held near one ear. (e) How does your answer compare to the earth's field, which is about $50 \mu \mathrm{T} ?$

Key Concepts

Magnetic Field from a Current Loop

A current loop generates a magnetic field that can be estimated using principles from magnetostatics, typically involving the Biot–Savart law. Modeling components like speakers as current loops helps in approximating the magnetic fields produced by everyday electronic devices, which is important for understanding their interaction with the environment.

Comparison of Magnetic Field Magnitudes

Comparing magnetic fields, such as that generated by a cell phone to the Earth’s magnetic field, involves analyzing relative magnitudes. This comparison helps in putting the strength of device-generated fields in context, shedding light on potential impacts, interference issues, and safety concerns related to electromagnetic exposure.

Fermi Estimation

Fermi estimation is a problem-solving technique used to arrive at rough, order-of-magnitude answers by breaking down complex problems into simpler, manageable estimates. This method is particularly useful in physics and engineering where exact numbers are less critical than understanding scale and magnitude.

Electric Power, Voltage, and Current

The relationship between electric power, voltage, and current is fundamental in circuit theory and electronics. Using the equation P = VI, one can determine the current drawn by a device when the power and battery voltage are known. This concept is key to understanding battery performance and energy consumption in electronic devices.

Transmission Power

Transmission power refers to the amount of energy per unit time that a device, such as a cell phone, emits as radio waves. In communications, knowing the transmission power is crucial because it determines the effective range and quality of signal coverage while also influencing battery life and electromagnetic interference levels.

Transcript

00:01 All right, in this question, we're talking about the magnetic field created by a leap of current.

00:06 And in this particular scenario, we're modeling the speaker on a phone as a current leap, and we're going to try to find the magnetic field at the center of someone's head.

00:19 So we start off by looking up the power created by a cell phone.

00:26 And for my particular phone, it was two watts.

00:32 There are going to be a lot of estimations or inconsistencies in this problem, the different numbers you might have depending on how you estimate things.

00:41 So don't really worry about it.

00:42 They're just looking for order of magnitude, sort of.

00:45 So we're just going to go two watts, even though yours might be a little different.

00:50 And then question b, they ask, what is the current created by the phone? and they tell us that the voltage is typically 1 .5 volts, and we know that power is equal to current times voltage, so the current is equal to power divided by voltage.

01:11 So we can plug in 2 and 1 .5, and we get that i is 4 over 3 amps.

01:21 Okay, so in question c, they ask us to estimate again.

01:25 This time they're asking us to estimate the width of a point.

01:27 Person said.

01:29 I just estimated this to be 0 .15 meters, although you might have gotten something pretty different.

01:37 And then question d asks us to estimate the diameter of a phone's speaker.

01:44 So looking at my phone, i thought it was a little bit less than millimeters, so i said 0 .08 or a little less than a centimeter.

01:57 Sorry, so yeah, 0 .08 meters.

02:01 And so that the radius of our current loop is going to be half of that, so 0 .04 meters.

02:11 And then they ask us to find magnetic field, which is created at the center of a person's head.

02:21 So if this is the phone speaker, maybe the phone is like sideways like this.

02:28 And this is the screen and the speakers up at the top...

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