# Electric Field Intensity An **electric field** is a region of space around an electric charge or a group of charges within which an electric force is exerted on other charged objects. This field concept, introduced by Michael Faraday, provides a way to describe how electric forces are transmitted through space. ## 1. The Electric Field and Force A source charge ($Q$) creates an electric field in the space surrounding it. When another charge, often called a "test charge" ($q$), is placed in this field, it experiences an electric force ($\vec{F}$). The electric field is the intermediary that communicates the force from the source charge to the test charge. ## 2. Electric Field Intensity ($\vec{E}$) **Electric field intensity** (or simply the electric field) is a vector quantity that describes the strength and direction of the electric field at a specific point. **Definition:** The electric field intensity at a point is defined as the electrostatic force ($\vec{F}$) experienced by a unit positive test charge ($q$) placed at that point. **Formula:** $$ \vec{E} = \frac{\vec{F}}{q} $$ - **Magnitude:** The magnitude of the electric field ($E$) represents the force per unit charge. - **Direction:** The direction of the electric field vector ($\vec{E}$) at a point is the same as the direction of the force that would be exerted on a **positive** test charge placed at that point. - Electric fields point **away from** positive source charges. - Electric fields point **towards** negative source charges. ## 3. Electric Field of a Point Charge We can derive the formula for the electric field created by a single point source charge ($Q$) by using Coulomb's Law. 1. The force ($F$) exerted by a source charge $Q$ on a test charge $q$ at a distance $r$ is: $$ \vec{F} = k \frac{Qq}{r^2} \hat{r} $$ 2. Using the definition of the electric field, $\vec{E} = \vec{F}/q$, we divide the force by the test charge $q$: $$ \vec{E} = \frac{1}{q} \left( k \frac{Qq}{r^2} \hat{r} \right) $$ 3. This gives the formula for the electric field intensity due to a point charge $Q$: $$ \vec{E} = k \frac{Q}{r^2} \hat{r} $$ Where $\hat{r}$ is a unit vector pointing from the source charge $Q$ towards the point where the field is being measured. This formula shows that the electric field strength decreases with the square of the distance from the source charge. ## 4. Units of Electric Field Intensity From the defining equation ($E = F/q$), the SI unit of electric field intensity is **Newtons per Coulomb (N/C)**. It is also commonly expressed in **Volts per meter (V/m)**. ## Example Calculation **Problem:** A point charge of $q = 9 \, \mu\mathrm{C}$ is located at the center of a sphere with a radius of $r = 3.0 \, \mathrm{m}$. Find the electric field intensity at the surface of the sphere. **Solution:** 1. **Identify the formula:** The magnitude of the electric field from a point charge is $E = k \frac{|q|}{r^2}$. 2. **Identify the values:** - $k = 9 \times 10^9 \, \mathrm{N} \cdot \mathrm{m}^2 / \mathrm{C}^2$ - $q = 9 \, \mu\mathrm{C} = 9 \times 10^{-6} \, \mathrm{C}$ - $r = 3.0 \, \mathrm{m}$ 3. **Substitute and calculate:** $$ E = (9 \times 10^9) \frac{9 \times 10^{-6}}{(3)^2} = (9 \times 10^9) \frac{9 \times 10^{-6}}{9} $$ $$ E = 9 \times 10^{9-6} \, \mathrm{N/C} = 9 \times 10^3 \, \mathrm{N/C} $$ The electric field intensity at the surface of the sphere is **$9 \times 10^3 \, \mathrm{N/C}$**, directed radially outward. ## Possible Questions and Answers - **Q:** What is the difference between an electric force and an electric field? **A:** An **electric field** is a property of space created by a source charge. It exists at every point, whether or not there is another charge present to feel it. An **electric force** is the interaction between an electric field and a second charge placed within it. The force only exists when there are at least two charges. - **Q:** What is a "test charge"? **A:** A test charge is a hypothetical charge with a very small magnitude. It is used to probe or measure the electric field at a point without significantly disturbing the field created by the source charges.