There are new scare stories circulating saying that mobile phone masts on schools are bad for children's health. There is plenty of scientific evidence that low levels of exposure to radio transmissions have no harmful effects, but in fact even if we assume that there are dangers, having a mobile phone mast on a school can be safer than not having one there.

Let us assume that in our hypothetical school, children:

- spend eight hours per day at school
^{1}, - spend all day at an average distance of twenty metres from the mast,
^{2} - make three five minute phone calls during the day with their mobile phones to their ears
^{3}, and - spend the rest of the time with their mobile phones one metre from them.
^{4}

Let us also assume that:

- the mast puts out a constant signal of 1 kilowatt
^{5}, and - the mobile phones communicate with the mast for five seconds every ten minutes, or
- the mobile phones communicate with the mast continuously when a phone call is in progress.

We will assume that the mast has been built for a reason, so that coverage is difficult if the mast is not present, and that only a child's own phone will affect them^{6}.

In this study I will be using ad-hoc figures for exposure based on the power of the transmission, the distance to the transmitter and the time taken. These units are related to a one hour exposure to a one watt transmitter at a distance of one metre^{7}. A little maths can easily convert that into proper exposure measurements, but my aim here is only to show the relative levels of exposure in various scenarios. The extra maths would just get in the way^{8}

# With No Mast

If there is no mast, then the mobile phones will be using full power, 4 watts, to communicate with the nearest mast. The child's exposure is the sum of:

- 8 hours at 1 metre from the phone, with the phone active for five seconds every ten minutes
- 15 minutes at 3cm from the phone, with the phone active continuously.

Five seconds every ten minutes is $\frac {5} {60 \times 10} = 0.0083$ of the time, $8 hours \times 0.0083 = 0.06 hours$. The output is four watts, so that is $0.067 \times 4 = 0.268$ in our ad-hoc units.

The exposure changes with the inverse square of the distance from the transmitter, so during a phone call the distance is only 3cm, or 0.03m, and that will increase the exposure by a factor of $\frac {1} {0.03^2} = 1111$ but only for a quarter of an hour a day, so that is an exposure of 277.75 per watt, for a total of 1111.

So the child's total exposure over the school day is $1111.3$ of our ad-hoc units.

# With A Mast

If there is a mast, then the mobile phones will be using their minimum power, $\frac 1 4$ watts. That reduces the exposure due to the phone to $\frac 1 4 \div 4 = \frac 1 {16} th$ of the previous case: 69.4

But then we have to add in the effect of the mast: a continuous signal of 1000 watts at a distance of 20 metres. $\frac {1000} {20^2} = 2.5$ for eight hours: $2.5 \times 8 = 20$

So the child's total exposure over the school day is $69.4 + 20 = 89.4$ of our ad-hoc units.

# What about texting?

Let's say fifty texts a day, each taking five seconds to send, with the phone half a metre away. So the distance effect is $\times 4$ and the time is $50 \times \frac 5 {60 \times 60} = 0.07$ hours. So at full power, $4 \times 4 \times 0.07 = 1.1$ and at minimum power, $\frac 1 4 \times 4 \times 0.07 = 0.07$.

Either way, texting does not make much difference.

# Speaker-phone?

Speaker-phone is much better. That makes the distance during a phone call about a quarter of a metre. So the effect of the distance is $\frac 1 {0.25^2} = 16$ per hour per watt.

So a quarter of an hour per day at maximum power would be an exposure of 16, and the same time at minimum power would be 1.

# So what have we learned?

- The effect of using a mobile phone is much more important than where the nearest mast is, even if it is very close.
- A close mast makes the phone use a lower power, which reduces exposure.
- Using speaker-phone reduces exposure significantly.

# Conclusion

I am not saying that mobile phone masts should be installed for the good of our children. This rough calculation can not hold such responsibility, nor does it take into account any medical evidence. I am not an expert in radiology or the effects of radiation on the human body.

However what this calculation has shown is that mobile phone masts do not significantly increase a child's exposure to electromagnetic radiation. Protesting a mobile phone mast in close proximity to a school is at best of questionable value, and at worst may be counter-productive.