Understanding Electric Field Intensity Made Easy

Electric field intensity is a key concept in electrostatics that quantifies the strength and direction of the electric field at a point in space due to a charged object. It is fundamental in understanding electric forces and potential within the region surrounding charges.

Definition of Electric Field Intensity

Electric field intensity at a point is defined as the electrostatic force experienced by a small positive test charge placed at that point, divided by the magnitude of the test charge. It describes both the magnitude and direction of the electric field at a specific location.

Mathematically, electric field intensity $\vec{E}$ is given by $\vec{E} = \dfrac{\vec{F}}{q}$, where $\vec{F}$ is the electrostatic force and $q$ is the test charge. The direction of $\vec{E}$ is the direction of the force on a positive test charge.

Electric field intensity is a vector quantity and its unit in SI is newton per coulomb (N/C). It is also commonly expressed in volts per meter (V/m).

Electric Field Intensity Due to a Point Charge

A point charge $Q$ generates an electric field intensity at a distance $r$ from itself, given by the formula $E = \dfrac{kQ}{r^2}$, where $k$ is Coulomb's constant $k = 1/(4\pi\varepsilon_0)$ in vacuum.

The direction of the electric field is radially outward from a positive charge and radially inward toward a negative charge. The magnitude of the electric field decreases sharply with increasing distance from the source charge.

The concept of electric field intensity forms the basis for evaluating the field due to multiple charges. In such cases, the total electric field at any point is determined by the vector sum of the fields produced by all individual charges present, applying the principle of superposition.

For a deeper understanding of how electric field patterns are visualized, refer to Electric Field Lines and Its Properties.

Electric Field Intensity Due to Continuous Charge Distributions

When dealing with continuous distributions of charge, such as a charged rod, plane, or sphere, the electric field intensity is calculated by considering charge density and integrating over the distribution.

The linear charge density $\lambda$ is defined as $\lambda = \dfrac{\Delta Q}{\Delta l}$. Surface charge density $\sigma$ and volume charge density $\rho$ are similarly defined for area and volume respectively. These concepts are essential when applying Gauss’s Law in various symmetries.

For methods related to the calculation of the electric field from a charged ring or infinite distributions, refer to Electric Field from a Charged Ring and Electric Field from an Infinite Plane.

Formula and Units of Electric Field Intensity

The electric field intensity formula is $E = \dfrac{F}{q}$, with $E$ in N/C or V/m, $F$ in newton (N), and $q$ in coulomb (C). Using force and charge, the dimensional formula becomes $[MLT^{-3}I^{-1}]$.

Force Experienced by a Charge in an Electric Field

A charge $q$ in an electric field of intensity $\vec{E}$ experiences a force $\vec{F} = q\vec{E}$. The force is parallel to $\vec{E}$ for a positive charge and antiparallel for a negative charge.

If a charged particle of mass $m$ is subjected to an electric field, it will accelerate with $a = \dfrac{qE}{m}$. The nature of this force does not depend on the velocity or position of the charge in a uniform field.

For more on extended charge configurations such as an infinite line of charge, see Electric Field from Infinite Linear Charge.

Relation Between Electric Field Intensity and Electric Potential

Electric field intensity is related to the rate of change of electric potential with respect to distance. The relationship is $E = -\dfrac{dV}{dr}$, where $dV$ is the potential difference and $dr$ is the distance between two points. The negative sign indicates that the field direction is in the direction of decreasing potential.

This relation shows that the electric field is maximum where the potential gradient is steepest. For comprehensive analysis of potential, visit Understanding Electric Potential.

Electric Field Intensity and Charge Density

In systems with continuous charge, electric field intensity calculations use charge density parameters—linear ($\lambda$), surface ($\sigma$), and volume ($\rho$). The total field at a location is obtained by integrating the effect of all infinitesimal charge elements, as derived in Gauss’s law and related applications.

Practical computation commonly refers to charge density for convenience, particularly in systems with symmetric charge distributions. For further concepts, refer to Charge Density Formula.

Properties of Electric Field Intensity

• Vector quantity with both magnitude and direction
• Independent of the test charge magnitude
• Direction defined as force direction on positive test charge
• Varies with position relative to source charge
• Follows principle of superposition for multiple charges

Electric Field Intensity Due to a Dipole

An electric dipole consists of two equal and opposite charges separated by a small distance. The electric field intensity at a point on the axial line of the dipole is $E_{axial} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{2p}{r^3}$, where $p$ is the dipole moment and $r$ is distance from the center.

On the equatorial line, the field is $E_{equatorial} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{p}{r^3}$, directed opposite to the dipole moment vector.

Difference Between Electric Field and Electric Field Intensity

Solved Examples on Electric Field Intensity

Example 1: Find the magnitude of the electric field at a distance of 1 m from a point charge of $30~\mu$C.

Solution: $E = \dfrac{kq}{r^2} = \dfrac{9 \times 10^9 \times 30 \times 10^{-6}}{1^2} = 2.7 \times 10^5~\text{N/C}$

Example 2: A $0.2~\mu$C charge placed in a field experiences a force of $4 \times 10^{-5}$ N. Find the electric field intensity.

Solution: $E = \dfrac{F}{q} = \dfrac{4 \times 10^{-5}}{0.2 \times 10^{-6}} = 200~\text{N/C}$