Demo: Force between two wires
- Two wires will carry current in opposite directions (L = down, R = up).
- What happens when current is run through the wires?
Observations
- The wires seem to twitch away from each other.
- The wires must be exerting a small, repulsive force on each other.
Explanation of force direction
- Imagine the left wire creates a B field. The current in the right wire experiences the B field.
- B field due to left wire, at right wire, is out of page.
- Force experienced by right wire = to right.
- Repeat to find force on left wire.
Explanation of magnitude
- r = 0.002 m
- I = 1.5 A for both wires
- L ~ 0.10 m
- B = μ0 I / (2 π r) = 1.5×10-4 T, for field at right wire due to left wire.
- F = B I L sin(θ) = 2.25×10-5 N
Notes: Velocity selector
- A device to only permit particles of a certain velocity through.
- The mass and charge of the particles are not important.
Set up
- A source of charged particles on the left.
- Charged particles first pass through a narrow opening.
- Then, they experience a downwards E field.
- + are deflected down, - are deflected up
- IF a B field into the board also fills the region, it by itself would deflect + up, - down.
- FE = q E
- FB = q v B
- An aperture on the right blocks all particles except those which are not deflected.
- The particles MUST have v = E / B
Questions
- If a + charge goes too slowly, which way will it be deflected? FE (down) > FB (up) → it is deflected down.
- If a - charge goes too fast, which way will it be deflected? FE (up) < FB (down) → down
Purpose
- E and B fields can be easily and precisely created (capacitor, solenoid)
- By controlling E and B, you can guarantee that the particles from a source have the same well known velocity.
Example: Velocity selector
- An electron passes through a velocity selector.
- The E field of the selector is 1200 N/C
- The B field of the selector is 0.04 T
- What is the speed of the electrons that make it through?
Solution
- v = E / B = 1200 N/C / 0.04 T
- T = N s / (C m)
- N/C / (N s / C m) = m / s
- v = 3.0×104 m/s
Notes: Charge in uniform B field
- A velocity selector emits charges into a region of uniform B.
- For simplicity, let B be the same as for the velocity selector.
Deflection
- + charge is initially deflected upwards
- Now that + charge is moving up / right, it is delfected up / left
- Now that it is moving up, it is deflected left
- ...
- Deflection is always perpendicular to velocity
- Because F is perpendicular to velocity, no work is done (v is constant)
- → uniform circular motion
UCM due to B field
- a = F / m = v2 / r
- F = q v B
- → q B / m = v / r
Example
- Protons travel 3.0×104 m/s to the right.
- They encounter a B field of .04 T into the board
- Will they go clockwise, or counter clockwise? (counter clockwise)
- How big is the circle they make? r = v m / (q B) = 7.97 mm