❓FAQs
❓Maxwell Stress Tensor and Surface Force❓How does the four-dimensional spacetime coordinate relate to the relativistic formulation of Maxwell❓What physical quantities are embedded in the four-vector (four-current density)?❓What are the sources for the inhomogeneous Maxwell's equations❓Why are Gauss's Law and the Ampère-Maxwell Law collectively called the inhomogeneous Maxwell's equat❓What two sources does the Ampère-Maxwell Law relate the curl of the magnetic field to?❓What is the result of analyzing the spatial components of the tensor equation?❓Which components of the tensor equation yield the Ampère-Maxwell Law?❓What two Maxwell's equations are unified by the single four-dimensional tensor equation?❓How does the single four-dimensional tensor equation unify Maxwell's equations?❓What is the physical meaning of the time component in the tensor equation?❓Which component of the tensor equation yields Gauss's Law?❓What is the final surface integral expression for the total magnetic force on a volume using the Max❓What is the explicit formula for the components of the magnetic Maxwell Stress Tensor in terms of th❓Write the i-th component of the total magnetic force as a surface integral using the explicit expres❓What is the physical interpretation of the Maxwell Stress Tensor that allows the magnetic force to b❓Which major vector calculus theorem is applied to convert the volume integral of the tensor's diverg❓What is the specific tensor notation for the Divergence Theorem used to go from the volume integral❓What is the gravitational tidal tensor?❓How is the differential acceleration in a gravitational field derived using Taylor expansion?❓What is the tidal force in physics?❓What is the expression for the tidal tensor in terms of the gravitational potential?❓What is the vector identity used to expand the centrifugal force formula?❓How can the centrifugal force be expressed using the angular velocity and the position vector after❓What is the form of the centrifugal force in component notation before identifying the tensor?❓What is the Hessian matrix of the gravitational potential?❓Is the gravitational tidal tensor symmetric?❓What is the formula for the gravitational potential outside a spherical mass distribution?❓How is the gravitational field calculated from the potential?❓What is the expression for the tidal tensor outside a spherical mass distribution?❓What is the form of the centrifugal force in component notation before identifying the tensor?❓In the linear tensor form, what is the explicit expression for the components of the tensor in terms❓Is the centrifugal force tensor symmetric?❓Under what geometric condition does the centrifugal force on a particle of mass vanish in a rotating❓What is the kinetic energy of mass moving in the horizontal plane?❓What is the kinetic energy of mass moving vertically?❓What is the total kinetic energy of the coupled mass system in terms of velocities of the generalize❓What are the generalized coordinates used for this system?❓What is the general formula for the components of the generalized inertia tensor?❓Why are the cross-terms zero?❓What is the component (radial inertia) of the generalized inertia tensor?❓What is the component (angular inertia) of the generalized inertia tensor?❓What is the final form of the generalized inertia tensor matrix M in generalized coordinates?❓What is the rotational identity for the moment of inertia tensor?❓What is the definition of the moment of inertia tensor used in the proof?❓How is the time derivative of the moment of inertia tensor calculated?❓How is the velocity vector related to the angular velocity and position in the proof?❓Why does the third term in the expression (the contraction between the time derivative of the inerti❓Why does the first term in the final expression for the Right-Hand Side vanish?❓What is the total electromagnetic force in a source-free static volume?❓Why is the total electromagnetic force zero in a source-free static volume?❓What is the force density of the electromagnetic field on matter (Lorentz force density)?❓What is the Maxwell stress tensor and how is it related to the total electromagnetic force?❓How do the static and source-free conditions simplify the expression for the total force on the ele❓What is the Maxwell stress tensor and how is it used to calculate the force on charges?❓How is the surface force on the field calculated in electrostatics?❓What is the total electric field on the plane equidistant from two equal charges separated by a dist❓How does the surface force on the field differ when the two charges are equal compared to opposite?❓In which direction does the surface force on the field point for two equal charges?❓What is the Coulomb force exerted by one charge on the other for two equal charges separated by 2d?❓Electric Field and Surface Force❓Force on Charges and Static Equilibrium❓How is the computed surface force on the field for equal charges verified using Coulomb's Law and th❓What is the relationship between the force on the charge and the total force on the field for static❓How is the anti-symmetry property used to show that the tensor product is symmetric in the free indi❓How is the Maxwell stress tensor expressed solely in terms of the magnetic field tensor by using the❓What is the final expression for the tensor product when computed in terms of the magnetic field com❓What is the formula for Young's modulus (E) in terms of bulk modulus (K) and shear modulus (G)?❓What is the formula for Poisson's ratio in terms of bulk modulus and shear modulus?❓How is the bulk modulus related to Young's modulus and Poisson's ratio?❓How is the shear modulus related to Young's modulus and Poisson's ratio?❓What are the full steps to derive the expression for Poisson's ratio from the constitutive equations❓What are the full steps to derive the expression for Young's modulus from the constitutive equations
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