Question about common math operations.

[zeromodz]

Okay say we know from magnetism.

E = F / q
F = KQq / R^2

Then we can say that.

E = KQq / (R^2 / q)

Then wouldn't we say
E = KQq * q / R^2
E = KQq^2 / R^2

Its just like saying.
5 / (1 / 2) = 5 * 2 / 1 = 10.

Why is it we cancel the q's instead of squaring them, because my textbook does that and ends up with this equation.
E = KQ / R^2

Because the answers are different. Thanks.

 

[Mark44]

Okay say we know from magnetism.

E = F / q
F = KQq / R^2

Then we can say that.

E = KQq / (R^2 / q)

No, we can't say this.
It's really E = (KQq/R^2) / q, which is the same as (KQq/R^2) * (1/q). The order in which you do the division is significant.

It might be easier to see formatted as it usually is in print.
$$E = \frac{F}{q} = \frac{1}{q} F$$
$$= \frac{1}{q} \frac{KQq}{R^2}$$
$$= \frac{KQ}{R^2}$$

The q factors cancel because you have one of them in a numerator and the other in a denominator.

Then wouldn't we say
E = KQq * q / R^2
E = KQq^2 / R^2

Its just like saying.
5 / (1 / 2) = 5 * 2 / 1 = 20.

This is not right, either. 5/(1/2) = 5*2 = 10

Why is it we cancel the q's instead of squaring them, because my textbook does that and ends up with this equation.
E = KQ / R^2

Because the answers are different. Thanks.