What Is The Magnetic Flux Density When The Vector Potential Is A Position Vector?

Explanation: The field intensity H = -Grad(V). Since the given potential is a position vector, the gradient will be 3 and H = -3. Thus the flux density

B = μH = 4π x 10

^{– 7}

x (-3) = -12π x 10

^{– 7}

units

.

How do you find the magnetic potential of A vector?

Calculating magnetic vector potential

d

A =4πrμ0​

I​ds . What is the magnetic vector potential a distance R R R from a long straight current element? r = R 2 + z 2 .

What is magnetic flux density when the vector potential is A position vector?

Explanation: The field intensity H = -Grad(V). Since the given potential is a position vector, the gradient will be 3 and H = -3. Thus the flux density

B = μH = 4π x 10

^{– 7}

x (-3) = -12π x 10

^{– 7}

units

.

How are magnetic vector potential and flux density related explain?

Magnetic vector potential: is a vector field that serves as the potential for the magnetic field. Thus, knowing the magnetic vector potential at a point, the flux density at that point can be

obtained

.

How do you find the current density of A magnetic vector potential?

So from the vector current density j, we can find A using Eq. (14.19)—that is, we find each component of A by solving three imaginary electrostatic problems for the charge distributions ρ1=j

x/c2

, ρ2=jy/c2, and ρ3=jz/c2. Then we get B by taking various derivatives of A to obtain ∇×A.

What is a potential vector field?

In vector calculus, a vector potential is a

vector field whose curl is a given vector field

. This is analogous to a scalar potential, which is a scalar field whose gradient is a given vector field.

What is the vector potential inside a solenoid?

In that case, we already know that the field inside the solenoid is uniform and is μnIˆz inside the solenoid and zero outside. Since the field has only a z component, the vector potential A can have only a φ- component.

A=12μnrIˆφ.

A=μna2I2rˆφ.

What is A vector potential used for?

. Together with the electric potential φ, the magnetic vector potential can be used

to specify the electric field E as well

. Therefore, many equations of electromagnetism can be written either in terms of the fields E and B, or equivalently in terms of the potentials φ and A.

How do you find the potential vector?

Show that the difference between your answer and the one obtained before has gradient zero. (3)

Let F = 〈y,z,x〉

. Show that F is divergence free; find a vector potential; then check your result. (4) Let F = 〈z2x − 1,−z2y,1 − x2〉.

Is vector potential physical?

The physical meaning of the electric scalar potential is usually considered to be potential energy per unit charge. The physical meaning of the magnetic vector potential is actually very similar:

it’s the potential energy per unit element of current

.

What is magnetic vector potential formula?

The vector A is called the magnetic vector potential. Its dimensions are MLT−1Q−1. Its SI units can be expressed as T m, or Wb m−1 or N A−1. It might be briefly noted here that some authors define the magnetic vector potential from H = curl A, though it is standard SI practice to define it from

B = curl A

.

Is vector potential unique?

As what you have explained,

magnetic vector potential is not uniquely determined

since there are an infinite number of equivalent vector potential A, for magnetic field B.

What is scalar potential of A vector?

This chapter defines scalar potential as the work done per unit charge by the electric field. The scalar potential is

the direct electrostatic analog of the gravitational potential energy per unit mass

. Scalar potential is used in electrodynamics when time-varying electromagnetic fields are present.

What is the direction of Poynting vector?

The direction of Poynting vector is

perpendicular to the direction of propagation of wave

. Explanation: The Poynting vector is proportional to the cross product of Electric and magnetic field, E X B. Therefore, its direction is perpendicular to Electric and Magnetic waves, i.e., in the direction of propagation of wave.

Is electric field A scalar or vector?

Electric field strength is a

vector quantity

; it has both magnitude and direction. The magnitude of the electric field strength is defined in terms of how it is measured.

Is magnetic field BA vector or A scalar?

Magnetic field has a polarity similar to the electric field but known as the North Pole and the South Pole. … Just like a vector quantity, a magnetic field is described with both magnitude and direction. Thus the magnetic field is

vector quantity

.