Question

The SI unit of displacement current is (A) coulomb (B) henry (C) ampere (D) faraday

Short answer

The SI unit of displacement current is (C) ampere.

Step-by-step solution

Identify the formula

The formula for displacement current (I_D) can be found using Maxwell's equations. The formula is given by: I_D = ε₀ * dφ_E/dt where ε₀ is the vacuum permittivity constant (measured in coulombs^2/newton-meter^2), dφ_E is the change in electric flux over time, and dt is the change in time. Step 2: Analyze the units in the formula

Analyze units

Since we are looking for the SI unit of displacement current, let's analyze the units in the formula: - ε₀ has the units of coulombs^2/newton-meter^2 - dφ_E has the unit of electric flux which is measured in volts * meters (V * m) or newtons * meters^2 / coulomb (N * m^2 / C) - dt has the unit of time, which is measured in seconds (s) Step 3: Determine the units for displacement current

Determine the units

Plug the units for ε₀, dφ_E, and dt into the displacement current formula: I_D = (coulombs^2/newton-meter^2) * (newtons * meters^2 / coulomb) / seconds Now simplify the units by canceling the newtons, meters^2, and one of the coulombs: I_D = (coulombs^1 / seconds) The resulting unit is coulombs per second, which is equivalent to the unit of electric current, the ampere (A). Therefore, the SI unit of displacement current is: (C) ampere

Key concepts

SI units

SI units, or International System of Units, are the standard units of measurement used globally in science and engineering. They include units such as meters for length, kilograms for mass, and seconds for time. In the context of electrical concepts, the ampere is the SI unit for electric current.

SI units help ensure consistent communication and application of measurements across various disciplines. When dealing with the displacement current, we use SI units to express quantities like electric charge in coulombs and current in amperes. This uniformity makes it easier to perform calculations and understand results among engineers and scientists worldwide.

Maxwell's equations

Maxwell's equations are fundamental equations in electromagnetism that describe how electric and magnetic fields interact. There are four equations, each detailing different electromagnetic principles.

• Gauss's law for electricity
• Gauss's law for magnetism
• Faraday's law of induction
• Ampere-Maxwell law

These equations unify electricity, magnetism, and light as manifestations of the electromagnetic field.

Understanding displacement current requires the Ampere-Maxwell law, which introduced the concept that a changing electric field can produce a magnetic field, analogous to how a moving electric charge creates a magnetic field. This addition by Maxwell allowed the equations to fully describe all electromagnetic phenomena, paving the way for modern electromagnetic theory.

Electric flux

Electric flux refers to the flow of the electric field through a given surface. It's a measure of the number of electric field lines passing through an area. The concept is similar to the flow of water through a net. If a lot of water goes through the net, we have high water flux. Similarly, if many electric field lines pass through a surface, the electric flux is high.

Electric flux is calculated using the formula: ${\varphi }_E=E\times A\times \cos (\theta )$
where $E$ is the electric field strength, $A$ is the area through which the lines pass, and $\theta$ is the angle between the field lines and the normal to the surface.

In the context of displacement current, changes in electric flux over time ($\frac{d{\varphi }_E}{dt}$) contribute to the production of a displacement current, linking the concepts of changing electric fields with magnetic fields.

Vacuum permittivity

Vacuum permittivity, also known as the electric constant and traditionally denoted as ${\epsilon }_0$, is a fundamental physical constant that characterizes the ability of the vacuum to transmit electric fields. It directly affects the force between electric charges in a vacuum, quantified by Coulomb's Law.

In terms of SI units, vacuum permittivity has the dimensions ${\text{C}}^2/\text{N}\cdot {\text{m}}^2$. This indicates it involves charge squared per unit force multiplied by area. It's a crucial factor in calculating displacement current.

Its value is approximately $8.854\times {10}^{-12}ext{C}^2/extN\cdot ext{m}^2$. This precise value allows for accurate predictions and calculations in various electromagnetic applications, making understanding this constant essential in physics and engineering.