as are other forms with . Integral form Gauss's law may be expressed as: where is the electric flux through a closed surface enclosing any volume , is the total charge enclosed within , and is the electric constant. The electric flux is defined as a surface integral of the electric field: where is the electric field, is a vector representing an infinitesimal element of area of the surface, and represents the dot product of two vectors. In a curved spacetime, the flux of an electromagnetic field through a closed surface is expressed as where is the speed of light; denotes the time components of the electromagnetic tensor; is the determinant of metric tensor; is an orthonormal element of the two-dimensional surface surrounding the charge ; indices and do not match each other. Since the flux is defined as an integral of the electric field, this expression of Gauss's law is called the integral form. In problems involving conductors set at known potentials, the potential away from them is obtained by solving Laplace's equation, either analytically or numerically. The electric field is then calculated as the potential's negative gradient. Gauss's law makes it possible to find the distribution of electric charge: The charge in any given region of the conductor can be deduced by integrating the electric field to find the flux through a small box whose sides are perpendicular to the conductor's surface and by noting that the electric field is perpendicular to the surface, and zero inside the conductor. The reverse problem, when the electric charge distribution is known and the electric field must be computed, is much more difficult. The total flux through a given surface gives little information about the electric field, and can go in and out of the surface in arbitrarily complicated patterns. An exception is if there is some symmetry in the problem, which mandates that the electric field passes through the surface in a uniform way. Then, if the total flux is known, the field itself can be deduced at every point. Common examples of symmetries which lend themselves to Gauss's law include: cylindrical symmetry, planar symmetry, and spherical symmetry. See the article Gaussian surface for examples where these symmetries are exploited to compute electric fields. Differential form By the divergence theorem, Gauss's law can alternatively be written in the differential form: where is the divergence of the electric field, is the