Electric Field (+ Field Strength) Simply Explained

The physical quantity electric charge \( q \) is the property of a charge carrier, for example, a particle (electron, proton) or a large electrically charged sphere from physics class. The charge indicates how well the charge carrier can interact electrically with other charge carriers. Interaction refers to how strongly the charge carrier is repelled or attracted by other charges. Depending on whether the charge carrier is positive (+) or negative (-) charged, it will be repelled (this happens with (+)(+) and (-)(-)) or attracted (this happens with (-)(+)).

The physical unit of charge is: 1 \[ [q] = \text{C} ~ (\text{Coulomb}) \]

Sometimes it is useful to express it in base SI units \( \text{C} = \text{As} \) (ampere-second) to simplify units in a calculation.

The physical quantity electric force \( F_{\text E} \) tells you how quickly the momentum \( p \) (i.e., the force) of a body changes when this force acts on that body. In our case, the body refers to a charge carrier with an electric charge \( q \). The momentum consists of the velocity \( v \) and the mass \( m \) of the charge carrier: \( p = m\,v\). Since the mass is usually constant (you don't change your mass when accelerating in a car), only the velocity \( v \) of the charge carrier changes over time when a force acts on it. When the velocity changes over time, the charge carrier accelerates (as you know from a car).

We speak of an electric force when it is caused by other charge carriers and not, for example, by pushing a charge carrier with one's hand (mechanical force). So, if there is a positively charged proton near a negatively charged electron, the electron experiences an electric force that accelerates it toward the proton.

The physical unit of force is: 2 \[ [F_{\text E}] = \text{N} ~ (\text{Newton}) \] As with the unit of charge, you can break down the unit of force into SI units to simplify the units in a calculation: \( \text{N} = \frac{\text{kg} \, \text{m}}{\text{s}^2} \).

You can easily calculate the magnitude of the electric field \( E \) (not to be confused with energy!) by observing how much force \( F \) acts per charge \( q \):

From equation 3, you can immediately read the unit of the electric field. With the unit of force 2 and the unit of charge 1, the unit of the electric field becomes: 4 \[ [E] = \frac{\text N}{\text C} ~ (\text{Newton per Coulomb}) \]

What is the difference between electric field / electric field strength?
In general, the electric field is a three-dimensional vector \( \boldsymbol{E} \), a arrow indicating the direction of the electric field. Its length (corresponding to the magnitude \( |E| \) of the electric field) is called electric field strength.

Typically, electric field is expressed in the unit \( [E] = \frac{\text V}{\text m} \) (volts per meter), which you can easily obtain through unit conversion.

To illustrate the electric field, electric field lines are used. Based on the field lines, you can determine in which direction a test charge would move if placed in the electric field. Field lines begin by definition at a positive and end at a negative charge.

The electric field of a uniformly positively charged sphere radiates outward radially. The field lines of the electric field originate from the positive sphere, as mentioned, and terminate at negative charges. In this case, these negative charges are located somewhere very far away (at infinity). Therefore, when drawing the field lines of a single charge, they are not visible in the image.

The field lines of a negatively charged sphere also run radially, but they point in the opposite direction—toward the negative charge. If you place a small test charge at any location in the electric field, this test charge will move along the field lines. The field lines indicate the direction of the force and thus the direction of motion of the test charge.

An interesting feature of the radial electric field of a sphere is that the individual field lines diverge more and more as you move away from the sphere. This is an indication that the electric force on a test charge decreases as it moves away from the sphere. The electric force on a test charge decreases quadratically with distance, as prescribed by Coulomb's Law. This means that if you halve the distance between the test charge and the charged sphere, the force on the test charge quadruples.

What would the field lines look like if you bring a negatively charged sphere near the positively charged sphere? The trajectory of the field lines will completely change! In this case, you get the electric field of a so-called electric dipole. The field lines still start at the positive and end at the negative charge, but a test charge would move completely differently in the field, unlike in the radial field of a single charge. The way such trajectories of field lines arise can be easily understood by considering the resulting force \(\boldsymbol{F}\) on the test charge.

Depending on how the field lines of the electric field run, the respective electric field is referred to as homogeneous or inhomogeneous.

• Homogeneous ("uniform") - intuitively means that the field lines have the same distance and alignment everywhere in space. Mathematically, this means: \( E = \text{const} \), so the electric field has the same value at every point. You can find such a homogeneous electric field between two electrically charged plates (parallel plate capacitor).
• Inhomogeneous ("non-uniform") - is exactly the opposite of "homogeneous". Such an inhomogeneous electric field is generated, for example, by a charged sphere. To indicate that the electric field depends on location, the position coordinate \( r \) is added: \( E(r) \). As in mathematics, \( E(r) \) is a function like \( f(x) \). Depending on the value of \( r \) you consider, the electric field (the value of the function) is different.