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Under what condition is a vector field considered conservative if the curl of the field is zero?
A vector field is considered conservative when its curl is zero.
Why electric field is zero when electrical potential is constant?
When the electric field is zero, it means there is no change in electrical potential across the field. In other words, the equipotential surfaces are parallel, indicating a constant electrical potential. This relationship arises from the fact that the electric field is the negative gradient of the electrical potential.
The potential is constant through a given region of space Is the electrical field zero or non zero?
If the potential is constant through a given region of space, the electric field is zero in that region. This is because the electric field is the negative gradient of the electric potential, so if the potential is not changing, the field becomes zero.
What is the relationship between the curl of a vector field and its representation in polar coordinates?
In polar coordinates, the curl of a vector field represents how much the field is rotating around a point. The relationship between the curl and the representation in polar coordinates is that the curl can be calculated using the polar coordinate system to determine the rotational behavior of the vector field.
The electrical intensity inside a charged hollow sphere is?
Zero, because the electric field inside a charged hollow sphere is zero. This is due to the Gauss's law and symmetry of the charged hollow sphere, which results in no net electric field inside the sphere.
Under what condition is a vector field considered conservative if the curl of the field is zero?
A vector field is considered conservative when its curl is zero.
Why electric field is zero when electrical potential is constant?
When the electric field is zero, it means there is no change in electrical potential across the field. In other words, the equipotential surfaces are parallel, indicating a constant electrical potential. This relationship arises from the fact that the electric field is the negative gradient of the electrical potential.
The potential is constant through a given region of space Is the electrical field zero or non zero?
If the potential is constant through a given region of space, the electric field is zero in that region. This is because the electric field is the negative gradient of the electric potential, so if the potential is not changing, the field becomes zero.
What is the relationship between the curl of a vector field and its representation in polar coordinates?
In polar coordinates, the curl of a vector field represents how much the field is rotating around a point. The relationship between the curl and the representation in polar coordinates is that the curl can be calculated using the polar coordinate system to determine the rotational behavior of the vector field.
Is the magnetic force an example of a nonconservative force?
Yes. For any vector field, force included, to be conservative, it must be irrotational, meaning that its curl must be zero everywhere. Fortunately (for me at least, since it makes this answer a whole heck of a lot easier to explain), the magnetic force field vector is already commonly expressed as a curl via Maxwell's equations:∇ X B = μ0J + μ0ε0∂E/∂t,where B is the magnetic field, μ0 is the permeability of free space, ε0 is the permittivity of free space, J is the current density, E is the electric field, t is time, and ∇ X B is the curl of the magnetic field. Bolded quantities are vectors.Now, if you don't know a thing about vector calculus, hopefully you at least remembered what I wrote above. For a vector field to be conservative, its curl must be zero everywhere. As you can hopefully see from that above equation, the curl of the magnetic field, ∇ X B, is not zero everywhere. More specifically, if there is a current density, J, within the magnetic field, or if there is a time changing electric field, ∂E/∂t, within the magnetic field, the curl of the magnetic field is not zero, therefore the magnetic force field is nonconservative.If you get lucky enough to find a situation where there is no current density or time dependent electric field, which is in reality impossible due to electrons providing there own time dependent electric fields, then the magnetic force field would be conservative.
Is curl of vector function F must perpendicular to every vector function f?
No, the curl of a vector field is a vector field itself and is not required to be perpendicular to every vector field f. The curl is related to the local rotation of the vector field, not its orthogonality to other vector fields.
The electrical intensity inside a charged hollow sphere is?
Zero, because the electric field inside a charged hollow sphere is zero. This is due to the Gauss's law and symmetry of the charged hollow sphere, which results in no net electric field inside the sphere.
Is the potential zero if the electric field is zero?
Yes, if the electric field is zero, then the electric potential is also zero.
If an electrical current passes through a conductor what two things are generated?
If an electrical current passes through a conductor, there is an induced voltage (because no conductor has perfectly zero ohms), resulting in power dissipation, and there is a magnetic field, which can interact with other conductors in the vicinity of the first.
How to find the direction of the magnetic field?
To find the direction of the magnetic field, you can use the right-hand rule. Point your right thumb in the direction of the current flow and curl your fingers. The direction your fingers curl represents the direction of the magnetic field.
Can you find a point where the electric field is zero?
Yes, the electric field can be zero at points where the net charge is zero or where the electric field vectors cancel each other out.
What is the right hand curl rule and how is it used to determine the direction of the magnetic field around a current-carrying conductor?
The right-hand curl rule is a method used to determine the direction of the magnetic field around a current-carrying conductor. To apply the rule, point your right thumb in the direction of the current flow. Then, curl your fingers around the conductor. The direction your fingers curl represents the direction of the magnetic field lines around the conductor.
