Animated Solution for Physics - Current Electricity: The potential difference applied to an X-ray tube is $5\text{ kV}$ and the current through it is $3.2\text{ mA}$. Then the number of electrons striking the target per second is

Imagine you are looking at an X-ray tube in action. We have a cathode emitting a steady stream of electrons towards a target. This entire process is driven by a potential difference of $5\text{ kV}$, which creates a measurable current of $3.2\text{ mA}$ flowing through the tube.

Our goal is to figure out exactly how many electrons are slamming into that target every single second.

To solve this, we need to go back to the absolute basics of electricity. What is electric current? It is simply the rate of flow of electric charge. Mathematically, we write this as:

But what exactly makes up this total charge $q$? It's not a continuous fluid; it's made up of discrete, tiny particles called electrons. Therefore, the total charge is the number of electrons ($n$) multiplied by the charge of a single electron ($e$). This is known as the quantization of charge:

Let's substitute our expression for total charge into the current equation. This gives us:

Since the question asks for the number of electrons striking the target per second, we can set our time interval $t$ to $1\text{ s}$. This simplifies our equation beautifully to:

Now, we just need to rearrange the formula to solve for $n$, the number of electrons:

Let's plug in the raw values provided in the problem. Remember to convert milliamperes to amperes! The current $i$ is $3.2\times 10^{-3}\text{ A}$, and the elementary charge $e$ is a fundamental constant, $1.6\times 10^{-19}\text{ C}$.

Dividing $3.2$ by $1.6$ gives us exactly $2$. For the powers of ten, dividing $10^{-3}$ by $10^{-19}$ gives us $10^{16}$.

So, a staggering $2\times 10^{16}$ electrons strike the target every second!

Did you notice something interesting about this problem? We never used the potential difference of $5\text{ kV}$!

This is a classic trap in physics problems. The $5\text{ kV}$ potential difference determines the kinetic energy of the electrons when they hit the target (which dictates the energy of the resulting X-rays), but it does not determine the number of electrons flowing per second. The number of electrons is solely determined by the current. Always trust your core principles and don't feel obligated to use every number given in a problem!