What is the unit of electric field intensity?

Short Answer:

The unit of electric field intensity is newton per coulomb (N/C). This means the electric field at a point is measured by the force (in newtons) experienced by a unit positive charge (in coulombs) placed at that point. It shows how strong the electric force is at that position.

Electric field intensity can also be expressed in volts per meter (V/m). Both N/C and V/m are equivalent and commonly used in physics and electrical engineering to describe the strength of an electric field in space.

Detailed Explanation:

Unit of electric field intensity

Electric field intensity is a physical quantity that tells us how strong an electric field is at a particular point. It describes the force that a unit positive test charge would experience when placed in the field. Since it deals with force and charge, the unit of electric field intensity is derived from these two basic quantities.

The basic definition of electric field intensity is:

E=FqE = \frac{F}{q}E=qF​

Where:

  • E is the electric field intensity
  • F is the force experienced by a test charge
  • q is the test charge

From this formula, the unit is:

Unit of E=Newton (N)Coulomb (C)=N/C\text{Unit of } E = \frac{\text{Newton (N)}}{\text{Coulomb (C)}} = \text{N/C}Unit of E=Coulomb (C)Newton (N)​=N/C

This means if a charge of 1 coulomb experiences a force of 1 newton, then the electric field intensity at that point is 1 N/C.

Alternate unit: volts per meter

Electric field intensity can also be expressed using electric potential:

E=VdE = \frac{V}{d}E=dV​

Where:

  • V is the potential difference (in volts)
  • d is the distance (in meters)

From this formula:

Unit of E=Volt (V)Meter (m)=V/m\text{Unit of } E = \frac{\text{Volt (V)}}{\text{Meter (m)}} = \text{V/m}Unit of E=Meter (m)Volt (V)​=V/m

So, N/C and V/m are equivalent units. Both represent the same quantity, and either can be used depending on the context. In electrostatics, N/C is commonly used, while in electric circuits and field strength applications, V/m is often used.

Relationship between N/C and V/m

Let us see how both units are the same:

We know:

1 Volt=1 Joule per Coulomb (J/C)and1 Joule=1 Newton⋅Meter (N\cdotpm)1 \, \text{Volt} = 1 \, \text{Joule per Coulomb (J/C)} \quad \text{and} \quad 1 \, \text{Joule} = 1 \, \text{Newton} \cdot \text{Meter (N·m)}1Volt=1Joule per Coulomb (J/C)and1Joule=1Newton⋅Meter (N\cdotpm)

So,

1 V/m=1 J/C1 m=1 N\cdotpm/C1 m=1 N/C1 \, \text{V/m} = \frac{1 \, \text{J/C}}{1 \, \text{m}} = \frac{1 \, \text{N·m/C}}{1 \, \text{m}} = 1 \, \text{N/C}1V/m=1m1J/C​=1m1N\cdotpm/C​=1N/C

This proves that both N/C and V/m are the same in value and meaning.

Practical understanding

  • In electrostatics, we use N/C to talk about the force a charge feels.
  • In electric fields between plates (like in capacitors), we often use V/m because it’s easier to measure voltage and distance.

For example, if a uniform electric field exists between two parallel plates 0.1 meters apart with a voltage of 10 volts, the electric field intensity is:

E=Vd=100.1=100 V/m=100 N/CE = \frac{V}{d} = \frac{10}{0.1} = 100 \, \text{V/m} = 100 \, \text{N/C}E=dV​=0.110​=100V/m=100N/C

Conclusion:

The unit of electric field intensity is newton per coulomb (N/C), which measures the force per unit charge. It can also be expressed as volt per meter (V/m) since both represent the same physical quantity. Understanding these units helps in measuring and analyzing electric fields accurately in both theory and real-world applications.