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How do you express the electric field due to a point charge in cylindrical coordinates?
The electric field due to a point charge in cylindrical coordinates can be expressed as ( \vec{E} = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r} \hat{r} ), where ( q ) is the charge, ( r ) is the radial distance from the point charge, and ( \hat{r} ) is the unit vector in the radial direction.
In which direction is the electric field on the cylindrical Gaussian surface oriented?
The electric field on the cylindrical Gaussian surface is oriented perpendicular to the surface, pointing outward or inward depending on the charge distribution inside the surface.
What is the relationship between vorticity and velocity in cylindrical coordinates?
In cylindrical coordinates, vorticity is related to the velocity by the curl of the velocity field. The vorticity vector is the curl of the velocity vector, which represents the local rotation of the fluid at a point in the flow.
What is the relationship between Gauss's Law, a cylindrical surface, and the electric field?
Gauss's Law states that the total electric flux through a closed surface is proportional to the total charge enclosed by that surface. When using a cylindrical surface to apply Gauss's Law, the electric field can be calculated by considering the symmetry of the surface and the distribution of charge within it. The relationship between Gauss's Law, a cylindrical surface, and the electric field allows for the determination of the electric field in a given scenario based on the charge distribution and geometry of the system.
What is the electric field inside an infinitely long cylindrical conductor with radius r and uniform surface charge density?
The electric field inside an infinitely long cylindrical conductor with radius r and uniform surface charge density is zero.
How do you express the electric field due to a point charge in cylindrical coordinates?
The electric field due to a point charge in cylindrical coordinates can be expressed as ( \vec{E} = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r} \hat{r} ), where ( q ) is the charge, ( r ) is the radial distance from the point charge, and ( \hat{r} ) is the unit vector in the radial direction.
In which direction is the electric field on the cylindrical Gaussian surface oriented?
The electric field on the cylindrical Gaussian surface is oriented perpendicular to the surface, pointing outward or inward depending on the charge distribution inside the surface.
What is the relationship between vorticity and velocity in cylindrical coordinates?
In cylindrical coordinates, vorticity is related to the velocity by the curl of the velocity field. The vorticity vector is the curl of the velocity vector, which represents the local rotation of the fluid at a point in the flow.
What is the relationship between Gauss's Law, a cylindrical surface, and the electric field?
Gauss's Law states that the total electric flux through a closed surface is proportional to the total charge enclosed by that surface. When using a cylindrical surface to apply Gauss's Law, the electric field can be calculated by considering the symmetry of the surface and the distribution of charge within it. The relationship between Gauss's Law, a cylindrical surface, and the electric field allows for the determination of the electric field in a given scenario based on the charge distribution and geometry of the system.
What is the electric field inside an infinitely long cylindrical conductor with radius r and uniform surface charge density?
The electric field inside an infinitely long cylindrical conductor with radius r and uniform surface charge density is zero.
A nonuniform electric field is directed along the x-axis. What is the net electrical flux passing the cylindrical surface?
The net electrical flux passing through a cylindrical surface in a nonuniform electric field is given by the integral of the electric field dot product with the surface area vector over the surface. The flux depends on the strength and direction of the electric field, as well as the shape and orientation of the surface.
What is the expression for the electric field in the perpendicular bisector plane of a dipole?
In the perpendicular bisector plane of a dipole, the electric field expression is given by: E = (kqd)/(r^3), where E is the electric field, k is Coulomb's constant, q is the magnitude of the charge at each end of the dipole, d is the separation distance between the charges, and r is the distance from the midpoint of the dipole.
How does the electric field between the capacitors change with their separation?
Electric field is got by the expression = charge density / epsilon not As so long charges on the plate remain the same the electric field also remains the same
What is the relationship between the electric field (E) and the rate of change of the electric potential (V) with respect to the distance (r), as described by the expression e dv dr?
The relationship between the electric field (E) and the rate of change of the electric potential (V) with respect to the distance (r) is described by the expression E -dV/dr.
How can Gauss's law be utilized to determine an expression for the electric field strength within a slab?
Gauss's law can be used to find the electric field strength within a slab by considering a Gaussian surface that encloses the slab. By applying Gauss's law, which relates the electric flux through a closed surface to the charge enclosed by that surface, one can derive an expression for the electric field strength within the slab.
Derive an expression for intensity of electric field at a point?
The intensity of an electric field at a point can be derived from Coulomb's law, which states that the electric field between two charges is directly proportional to the magnitude of the charges and inversely proportional to the square of the distance between them. Mathematically, the expression for electric field intensity (E) at a point is given by (E = \frac{k \cdot |q|}{r^2}), where (q) is the charge creating the field, (r) is the distance from the charge to the point, and (k) is the Coulomb's constant.
What is electrical anharmonicity?
Electrical anharmonicity refers to a term in the potential energy of a crystal which is linear in the externally applied electric field amplitude, and quadratic in lattice displacement coordinates. As such, it gives a dielectric polariztion which is quadratic in the lattice coordinates. Such an interaction term of lattice and external field allows the direct absorption of photons by two-phonon states of the crystal.
