Stokes and Maxwell Equations Quiz

The curl is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space.

If the curl of a vector field is zero, then the vector field is called irrotational.

Gauss’s divergence theorem relates the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed.

<p>If the divergence of a vector field is zero, then the vector field is called solenoidal.</p> Signup and view all the answers

<p>The curl of a vector field is a vector defined as the cross product of the del operator and the vector field.</p> Signup and view all the answers

<p>A vector field is irrotational if its curl is equal to zero.</p> Signup and view all the answers

<p>No magnetic monopoles exist in isolation; instead, the magnetic field is attributed to a dipole, and the net outflow of the magnetic field through a closed surface is zero.</p> Signup and view all the answers

<p>Displacement current density is given by $\mu_0\epsilon_0\frac{\partial E}{\partial t}$ in Ampere’s law with Maxwell’s correction.</p> Signup and view all the answers

<p>$\nabla \cdot E = \frac{\rho_e}{\epsilon_0}$</p> Signup and view all the answers

<p>$\nabla \times E = -\frac{\partial B}{\partial t}$</p> Signup and view all the answers

<p>$\nabla \times B = \mu_0J_e + \mu_0\epsilon_0\frac{\partial E}{\partial t}$</p> Signup and view all the answers

<p>Magnetic monopoles do not exist in nature as isolated north or south poles; instead, magnetic fields are represented as dipoles, and the total magnetic flux through a closed surface is always zero.</p> Signup and view all the answers

<p>The gradient represents the change in the scalar quantity with respect to distance. It is a vector perpendicular to the surface of constant scalar value.</p> Signup and view all the answers

<p>The divergence of a vector is a scalar quantity that represents the rate at which the vector field is spreading out or converging at a given point.</p> Signup and view all the answers

<p>The divergence of a vector shows how much the vector field is diverging or converging at a point. It helps understand the flow or spread of a vector quantity.</p> Signup and view all the answers

<p>Gauss's law states that the total electric flux through a closed surface is proportional to the total charge enclosed by the surface, divided by the permittivity of free space.</p> Signup and view all the answers

<p>Faraday's law states that a change in magnetic field induces an electromotive force (emf) in a closed circuit.</p> Signup and view all the answers

<p>Ampere's law states the relationship between magnetic field and electric current. Maxwell's correction adds the displacement current term to Ampere's law to account for changing electric fields.</p> Signup and view all the answers

<p>Magnetic monopoles are hypothetical particles that carry a single magnetic pole, either a north pole or a south pole, unlike in reality where magnetic poles always come in pairs.</p> Signup and view all the answers

<p>Displacement current density is a term introduced by Maxwell to account for the changing electric fields and their ability to induce magnetic fields.</p> Signup and view all the answers