Radiation, Magnetic fields and Linear Acceleration?

[NeroBlade]

Hi I've been revising and came across some questions which I do not understand how they obtained the answer could you guys help?

1.

Show that the momentum, p, of a particle of mass m is related to its kinetic energy, KE by the relationship p^2 = 2m KE

Use the above relationship to calculate the accelerating potential required for
electrons to have a de Broglie wavelength of 4·5 × 10^(–11) m.

And the answer turns out to be 645V.

2.

A magnet moves towards a coil as shown (solenoid circuit). Use Lenz’s law to explain in which direction the current will flow through the turns of the coil. The coil is now situated in a uniform magnetic field changing at a rate of 0·43Ts^–1.

r = 0.046m
B = 0.43Ts^-1
N = 1300
Total Resistance = 6.6 ohms
A = 2 *(pi)* r^2 = 0.0133m^2

Calculate the current flowing in the ammeter.

Formulas I've thought of is R = V/I, E = NBA / t and I set V = 1

However the formula turned out to be

I = (1300 * 0.43 * (pi) * ((0.046)^2)) / 6.8 = 0.55A

Problem I got is how did R become the demominator (6.8)?

3.

In the LINAC, the protons are accelerated from rest through 3 gaps each with an accelerating p.d. of 36kV.

KE in J is 1.7*10^(-14)J
Speed of protons 4.5 * 10^6 ms^-1

The radius of the synchrotron is 12·5 m. Calculate the value of the magnetic flux
density in the synchrotron when the speed of the protons is 9·4 × 10^6 ms^–1.

Equation I could think of is

F = (mv^2) / r where do I go from here?

Any help would be gr8

Cheers

 

[Astronuc]

In 3. what is the Lorentz force?

Also please show one's work.

 

[NeroBlade]

1.$Attempt$

KE by the relationship p^2 = 2m KE

Use the above relationship to calculate the accelerating potential required for
electrons to have a de Broglie wavelength of 4·5 × 10^(–11) m.

$$\lambda$$ = h/mv

since p^2 = 2m KE
$$\lambda$$^2 = h^2/(mv)^2
(mv)^2 = h^2 / $$\lambda$$^2 = 2m KE

This is the point I couldn't continue...


2. #Attempt#

r = 0.046m
B = 0.43Ts^-1
N = 1300
Total Resistance = 6.6 ohms
A = 2 *(pi)* r^2 = 0.0133m^2

Calculate the current flowing in the ammeter.

Formulas I've thought of is R = V/I,
E = NBA / t
and I set V = 1

Rearranging would give me

E = NB2(pi)r^2/t
E = IVt = NB2(pi)r^2/t

Rearranging and cancellation provides

I = NBA/Vt^2

However the formula turned out to be

I = NBA/R
I = (1300 * 0.43 * (pi) * ((0.046)^2)) / 6.8 = 0.55A

3. #Attempt#

Equation I could think of is

F = (mv^2) / r = BQv

F = (1.67 x 10^-27 x 9·4 × 10^6) / (12.5 x Q ) = B

Im sure that F= BQv but prob is I cannot find Q...

 

[dx]

$$\lambda$$ = h/mv

since p^2 = 2m KE
$$\lambda$$^2 = h^2/(mv)^2
(mv)^2 = h^2 / $$\lambda$$^2 = 2m KE

This is the point I couldn't continue...

Now write KE in terms of V. If an electron at rest is accelerated through a potential V, what is it's KE?

 

[NeroBlade]

The Kinetic Energy I worked out for the proton accelerated through 3 gaps with pd of 36kV is 108kEv which is 1.7 x 10^-14 J

 

[dx]

I was talking about your attempt at question 1.