FAQs

Maxwell Stress Tensor and Surface ForceHow does the four-dimensional spacetime coordinate relate to the relativistic formulation of MaxwellWhat physical quantities are embedded in the four-vector (four-current density)?What are the sources for the inhomogeneous Maxwell's equationsWhy are Gauss's Law and the Ampère-Maxwell Law collectively called the inhomogeneous Maxwell's equatWhat 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 MaxWhat is the explicit formula for the components of the magnetic Maxwell Stress Tensor in terms of thWrite the i-th component of the total magnetic force as a surface integral using the explicit expresWhat is the physical interpretation of the Maxwell Stress Tensor that allows the magnetic force to bWhich major vector calculus theorem is applied to convert the volume integral of the tensor's divergWhat is the specific tensor notation for the Divergence Theorem used to go from the volume integralWhat 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 afterWhat 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 termsIs the centrifugal force tensor symmetric?Under what geometric condition does the centrifugal force on a particle of mass vanish in a rotatingWhat 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 generalizeWhat 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 inertiWhy 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 eleWhat 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 distHow 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 ForceForce on Charges and Static EquilibriumHow is the computed surface force on the field for equal charges verified using Coulomb's Law and thWhat is the relationship between the force on the charge and the total force on the field for staticHow is the anti-symmetry property used to show that the tensor product is symmetric in the free indiHow is the Maxwell stress tensor expressed solely in terms of the magnetic field tensor by using theWhat is the final expression for the tensor product when computed in terms of the magnetic field comWhat 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 equationsWhat are the full steps to derive the expression for Young's modulus from the constitutive equations

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