For a solution to be a physical solution, it must satisfy several criteria. First, it must be continuous everywhere. Second, it
must have a continuous derivative everywhere, except for points where the potential energy becomes infinite (as it does at the walls of the box). Finally, it must be normalizable. In this case, you can check the first criterion by noting that the two functions Csin(nT/L) and 0 are continuous and that they have the same value at x = 0 and z = L, where their domains meet. To check the second criterion, simply take the first derivative of Csin(nTr/L) and 0. Both derivatives are continuous functions in their domains. The points where the domains meet are exactly the points where the potential energy becomes infinite, so you don't have to check for continuity there. The third criterion requires that there exist some value of C such that Since (z) is zero outside of the interval 0 < ¢ < L, this equation reduces to Use this equation to find the unique positive value of C. Express your answer in terms of L.
1 answer:
You might be interested in
Answer:
a) - the resistance is proportional to the length of the metal
- a thicker rod, since resistance decreases with increasing area
b) The current is proportional to the area so this is the factor that is influenced by the electric field
Explanation:
a) When the rod is connected to the rod an electrical circuit described by the expression is formed
V = I R
I = V / R
The resistance of the rod is
R = ρ L / A
Where ρ is the resistivity of metal, L Longitud and A cross section.
If a higher current is measured when the other rod is connected, it implies that the resistance has decreased. To have a decrease in resistance you have two possibilities
- use a shorter rod, since the resistance is proportional to the length of the metal
- Use a thicker rod, since resistance decreases with increasing area, remember that the area of a circle is
A = π R²
Therefore, small increases in the diameter of the rod could give great changes in resistance.
b) The current is defined with the charge that crosses a surface per unit of time, when the electric field increases the electrons feel a greater force, therefore the current increases.
The charge number on a wire is
Q = q n Δt A
So up to date is
I = q n When the rod is connected to the rod an electrical circuit described by the expression is formed
V = I R
I = V / R
The resistance of the rod is
R = rho L / A
Where rho is the resistivity of metal, L e; Long and A cross section.
If a higher current is measured when the other rod is connected, it implies that the resistance has decreased. To have a decrease in resistance you have two possibilities
.- use a shorter rod, since the resistance is proportional to the length of the metal
. - Use a thicker rod, since resistance decreases with increasing area, remember that the area of a circle is
A = pi R2
Therefore, small increases in the diameter of the rod could give great changes in resistance.
.b) The current is defined with the charge that crosses a surface per unit of time, when the electric field increases the electrons feel a greater force, therefore the current increases.
The load number on a wire is
Q = q n Dt A
So current is
I = q n v_{d} A
The drag speed (v_{d}) is constant in the materials, it depends on the purity and imperfections, so a change in the length does not significantly change the current.
The current is proportional to the area so this is the factor that is influenced by the electric field
The drag speed (vd) is constant in the materials, it depends on the purity and imperfections, so a change in the length does not significantly change the current.
The current is proportional to the area so this is the factor that is influenced by the electric field