An electric field is A a scalar function of space B a scalar function of space and time C a vector function of space D a vector function of space and time E none of these What about a magnetic field?
The expressions for the energy density and pressure of a scalar field o are (Ryden, Chapter 10): 66 = 5382 +V(6) Pa = 11 1512 - V(6) (0) (3) 2 ħc3 By subsituting these expressions into the fluid equation (€ +31(t)[€+p] = 0), show that you obtain the "equation of motion”, analogous to a ball rolling down a hill, with friction proportional to its speed, ©+3H (t)º = -ħc34 do (4)
Consider the vector field a(r) = re+ (CT) Show that a is irrotational Find a scalar potential φ for a and verify that it satisfies a = C.
1) (a) The conjugation function on C" is NOT a linear transformation when the scalar field is C, for any positive integer n. However, it IS true when the scalar field is R. Show that the conjugation function T:C" C", where T () = 7 is a linear transformation for the vector space Cover R. (b) Show that CR2m as vector spaces over R.
1. point charge equivalently show that the scalar potential and electric field of a moving with constant velocity a can be written Ver, t = t 9 - 4TE0 R (1-v²sn²0/0²) as Ecř, t) - Site ATTEO (1-r*sino/) / R = r _ vt
Q) use the laplace equation to find the electric field of the
capacitor
++tt d Vo(itial Voltase) 내느
++tt d Vo(itial Voltase) 내느
the excercise concerns the function (x^2 + y^2)* e^(1-x^2 -
y^2)
please do all parts
MA330 Homework #4 1. This exercise concerns the function its gradient vector field F-vo See the plots of each below. a) Compute the partial derivatives os and ty to find the gradient field vo. (b) In MA231, learned 1, you learned that mixed second-order partial derivatives of reasonable functions Verity that here by computing day and dys and checking that they are the same. should...
4. We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field that satisfies: Of course, not all vector fields can be written as the gradient of a scalar function. (a) Show that the electric field given below is not the result of an electrostatic potential (b) Just because this electric field can't come from an electrostatic potential, it doesn't mean it can't exist - it just can't be created by static...
We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field that satisfies: Of course, not all vector fields can be written as the gradient of a scalar function. (a) Show that the electric field given below is not the result of an electrostatic potential. E(x, y, z) = ( 3.0m,2 ) ( yi-TJ (b) Just because this electric field can't come from an electrostatic potential, it doesn't mean it can't exist...
Could you please answer both and show work?
1.13.10 With E the electric field and A the magnetic vector potential, show that [E + aA/ai] is irrotational and that therefore we may write 0t 1.13.11 The total force on a charge q moving with velocity v is Using the scalar and vector potentials, show that Exercise 1.13.10