E through G. Need different opinion. Please write legibally or put in digitally.

Question

E through G. Need different opinion. Please write legibally or put in digitally. Really important this is fully correct. Thanks

Insulating region -p -p A long thin wire with charge per unit length t2 is embedded within a long cylinder of negatively charged insulating material with charge per unit volume -p. The cylinder has radius R and the wire is sufficiently thin that you can ignore its radius. The figure above shows the cross section of the wire and cylinder and a cutaway showing the wire embedded inside the cylinder in 3ID The cylinder is the same length as the wire. a) What is the total charge enclosed, qn, within a Gaussian cylinder with radius ( R)and length L centered along the axis of the wire? (3 pts) b) Since the insulator and the wire have opposite charges, what do you notice about your expression for the charge enclosed, gim? What value of r (let's call this rcrit) makes the total charge enclosed by the Gaussian cylinder zero? (3 pts) c) Using your Gaussian cylinder, find the electric field inside the insulating cylinder for the case where R. (3 pts) d) If R is greater than rcrit, what value ofr makes the electric field equal to zero? (1 pt) e) What is the electric field outside the cylinder (r>R) as a function of r? (3 pts) f) Now imagine that we have a proton with charge te. If the proton is a long ways away from the cylinder, what is the force that the cylinder exerts on the proton? Assume that R >rerit. 3 pts) If the proton is released from a long ways away from the cylinder and wire with no other forces acting on it, describe in qualitative terms how it will behave due to the forces that the cylinder and wire exert on it. In what regions is it attracted to the cylinder? Where is the force zero? Where is it repelled from the cylinder? You can assume that the proton is free to move within the insulator because it is so small. (4 pts) g)

Explanation / Answer

According to the question

We know that

Charge per unit length in wire = lambda

charge per unit volume in cylinder = -rho

radius of cylinder = R

Then,

A)

Consider a gaussean surface at r < R

length of gaussean surface cylinder = L

so enclosed charge qen = (lambda*L - rho*pi*r^2*L) = L(lambda - pi*r^2*rho)

Then,

B)

As the enclosing charge is -ve and the charge on wire is +ve, the qenc has a sign that depends on r

so when qenc = 0

lambda = pi*r^2*rho

r = sqroot(lambda/pi*rho)

Then,

C)

From gauss' law

E*2*pi*r*L = qenc/epsilon [ where epsilon is permittivity of free space]

so for r < R

E = (lambda - pi*r^2*rho)/2*pi*epsilon

Then,

D)

For R > sqroot(lambda/pi*rho)

there is no value of r for which E will be 0, except for r -> infinityo

Then,

E)

For r > R

qenc = (lambda*L - rho*pi*R^2*L)

so E*2*pi*r*L = (lambda*L - rho*pi*R^2*L)/epsilon

E = (lambda - rho*pi*R^2)/epsilon**2*pi*r

Then,

G)

First protyon will start to move towards the wire with increasingspeed.

when it reaches at r = r_crit, it has maximum speed after that still it will move towards the wire but speed will strat to decrease.

then it will stop at some distance from wire then it will start moving away from wire with increasingspeed till r = r crit.

after that speed willl start to decrease and it will stop at the initial position and will follow this again and again(Oscillatory motion )

force zero at r = r_crit.

attractive force: r > r_crit

repulsive force: r < r_crit

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.