Motion in a Magnetic Field and TV

In summary, the conversation discusses the use of magnetic deflection coils in an old black and white TV and how to calculate the necessary field magnitude to deflect an electron beam to the side of the screen. The conversation also includes the equations and calculations used to solve the problem, with a comparison to the solution provided in the book.
  • #1
MickOtto
4
0

Homework Statement



The Picture tube in an old black and white TV uses magnetic deflection coils rather than electric plates. Suppose an electron beam is accelerated from rest through a 50kV potential difference and then through a region with uniform magnetic field 1cm wide. The screen is located 10cm from the coils and is 50cm wide. When the field is off, the electron beam hits the centre of the screen. Ignoring relativistic corrections, what field magnitude is needed to deflect the beam to the side of the screen.

m_e = 9.11E-31 kg;
q_e = 1.6E-19 C;
delta V = 50E3 V;
d_1 = 0.01m
d_2 = 0.1m
d_3 = 0.5m

Homework Equations



F = qv x B = qvBsin(theta) = qvB (assuming the magnetic field is at right angles);
1/2mv^2 = q*deltaV;
F = ma;
v_f = v_i + at;
v=d/t

The Attempt at a Solution



I will say the velocity from the potential difference is positive x and screen to be in the yz plane. I also assume the magnetic field is pointed in the positive z direction, giving the velocity from magnetic field in the y direction.


First I got the velocity from potential difference.

1/2mv^2=qV
=> v = sqrt(2q_eV/m_e)

Then I worked out the velocity in y from magnetic field, I'll call this v'.

F = qvB = ma
=> a=qvB/m.
v'_f = v'_i + at v'_i = 0;
v'_f = at =qvBd_1/mv = qBd_1/m_e (using t = d_1/v)

Now, time taken for beam to travel 0.1m in x is

t = d/v = 0.1/sqrt(2q_eV/m_e) = 7.5E-10

Beam must travel d_3/2 = 0.25m in this time, so v' = d/t becomes

0.25/7.5E-10 = 3.3E8.

We have v' = qBd_1/m_e.

Rearranging I got

B = m_e v/q_e d_1.

Plugging in numbers I get B =0.18 T.

The answer the book gives is 70 mT.





In the solutions the book works out R as a radius of curvature from Pythagorus and uses qvB=mv^2/R. My problem with this is that the magnetic field only exists for 0.01m, not 0.1m which is what they use.


Any help/pointing out the obvious and making me feel like an idiot will be greatly appreciated.


Thanks,
Michael.
 
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  • #2
Ok, I see what they do in the solutions now.

They use trig and get R for the magnetic field (giving it value 1.08cm) the use qvB=mv^2/R, solve for B and get the answer. I know my way is a lot messier than that, but why doesn't it work?
 

What is the relationship between motion and magnetic fields?

Motion in a magnetic field is influenced by the presence of a magnetic field. The direction and magnitude of the magnetic field can alter the trajectory and speed of a moving object.

How do magnetic fields affect TV signals?

Magnetic fields can interfere with the transmission of TV signals. This can cause disruptions in the reception of the signal, resulting in a distorted or low-quality image on the TV screen.

How do scientists study motion in a magnetic field?

Scientists use mathematical equations and experiments to study the effects of magnetic fields on motion. They also use specialized tools such as magnetic sensors and computer simulations to analyze and understand the behavior of objects in a magnetic field.

Can magnetic fields affect the functioning of a TV?

Yes, magnetic fields can affect the functioning of a TV. The magnetic field can disrupt the electronic components of the TV, causing malfunctions or even permanent damage.

What are some real-life applications of motion in a magnetic field and TV?

Motion in a magnetic field has various real-life applications, such as in the operation of electric motors, generators, and transformers. It also plays a crucial role in the functioning of particle accelerators and MRI machines. TV technology also relies on magnetic fields for the transmission and reception of signals, making it an essential part of our daily lives.

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