Question

3. (10 pts.) One often forgets the curl has a physical meaning. The curl operator differs from the divergence field to produce another field. Since vectors are more operator in that it acts on a_ complicated than scalars it is important to understand the purpose of the curl operator. Let E (r.y, :) be some electric field. The mathematical expression for the curl of is written as ex ey e .az _ ax)s+(a --dy)互 az广ㄨ oy The physical significance of the curl operator is that it describes the "rotation" of the field E at a point in question. Imagine the electromagnetic radiation from a cell phone as pictured below. Notice the strength of the field at any point (x, y) is equal to E(r, y). The direction of the curl points in the z-direction (out of the page) and measures its rotation or "curl" as a z-component as shown below. The ficld diminishes as you get further from the cell phone. Question: Now suppose you consider the curl in the exact center (4 field line from the right). Then comparing the field lines on both sides of the center, one side of the field has more intense radiation/flow. Compute precisely the curl of this vector field at the center of the field lines. From Maxwell's equations, write down the magnetic field using Faraday's Law. Note I did not say prove the magnetic field, just show the expression(s).

answer both please

Answer 1

The curl has a physical meaning different The curl operator describes rotation of a vector Non-zero curl we have, nabla^bar times v^bar = (partial differential V_z/partial differential y - partial differential V_x/partial differential z)e_x^^+ (partial differential V_x/partial differential z - partial differential V_z/partial differential x)e^^y = (partial differential V_y/partial differential x - partial differential V_z/partial differential y)e_z^^in one condition \r\n Then partial differential V_x/partial differential x, partial differential V_x, partial differential y, partial differential V_x/partial differential z will not be zero hence from equation (i) nabla^bar times v^bar partial differential V_x/partial differential z E_y^^= partial differential V_x/partial differential y e_z^^more force than the top the shaft will rotate counter clockwise with axis along the z direction.