An electron is travelling at 3.0 \(\times\) 10\(^{6}\) m s\(^{-1}\) in the path shown.
Calculate the magnetic field required to keep the electron in the path. (3 marks)
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An electron is travelling at 3.0 \(\times\) 10\(^{6}\) m s\(^{-1}\) in the path shown.
Calculate the magnetic field required to keep the electron in the path. (3 marks)
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\(1.7 \times 10^{-6}\) \(\text{T}\)
→ The force from the magnetic field on the electron provides the centripetal acceleration for it to travel in uniform circular motion.
\( F_B\) | \(=F_c\) | |
\(qvB\) | \(=\dfrac{mv^2}{r}\) | |
\(B\) | \(=\dfrac{mv}{qr}\) | |
\(=\dfrac{9.109 \times 10^{-31} \times 3.0 \times 10^6}{1.602 \times 10^{-19} \times 10}\) | ||
\(=1.7 \times 10^{-6}\) \(\text{T}\) |
→ Magnetic field strength required = \(1.7 \times 10^{-6}\) \(\text{T}\).
A particle of mass `m` and charge `q` travelling at velocity `v` enters a magnetic field of magnitude `B` and follows the path shown.
A second particle enters a magnetic field of magnitude `2B` with a velocity of `(1)/2 v` and follows an identical path.
What is the mass and charge of the second particle?
`C`
→ The centripetal force acting on the charge is given by the force it experiences due to the magnetic field:
`F_(c)` | `=F_(b)` | |
`(mv^2)/(r)` | `=qvB` | |
`r` | `=(mv)/(qB)` |
Given `B=2B` and `v=(1)/(2)v`:
`r` | `=(m(1)/(2)v)/(q(2B))` | |
`r` | `=(mv)/(4qB)` |
→ In order for the radius to remain the same, `(m)/(q)` must be four times what it was originally.
`=>C`
An electron moves in a circular path with radius `r` in a magnetic field as shown.
If the speed of the electron is increased, which row of the table correctly shows the effects of this change?
`B`
→ Using the formula `F=qvB`, increasing the speed of the electron increases the force acting on it.
→ The centripetal force acting on the electron is given by the force it experiences due to the magnetic field:
`(mv^2)/(r)=qvB\ \ =>\ \ r=(mv)/(qB)\ \ =>\ \ r prop v`
→ Increasing the speed of the electron increases its radius.
`=>B`
A proton and an alpha particle are fired into a uniform magnetic field with the same speed from opposite sides as shown. Their trajectories are initially perpendicular to the field.
Explain ONE similarity and ONE difference in their trajectories as they move in the magnetic field. (4 marks)
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Similarity:
→ Both particles experience a constant force, given by `F=qvB`, perpendicular to their velocity and the magnetic field lines and will undergo circular motion.
Difference:
→ The centripetal force acting on both particles is given by the force they experience due to the magnetic field as follows:
`(mv^2)/(r)=qvB\ \ =>\ \ r=(mv)/(qB)`
→ The alpha particle has four times the mass and two times the charge of the proton
→ Therefore, the radius of its trajectory will be twice that of the protons.
Similarity:
→ Both particles experience a constant force, given by `F=qvB`, perpendicular to their velocity and the magnetic field lines and will undergo circular motion.
Difference:
→ The centripetal force acting on both particles is given by the force they experience due to the magnetic field as follows:
`(mv^2)/(r)=qvB\ \ =>\ \ r=(mv)/(qB)`
→ The alpha particle has four times the mass and two times the charge of the proton
→ Therefore, the radius of its trajectory will be twice that of the protons.
A metal cylinder is located in a uniform magnetic field. The work function of the metal is `phi`.
Photons having an energy of 2`phi` strike the side of the cylinder, liberating photoelectrons which travel perpendicular to the magnetic field in a circular path. The maximum radius of the path is `r`.
If the photon energy is doubled, what will the maximum radius of the path become?
`D`
`K_max` | `=(1)/(2)mv_(max)^2` | |
`v_(max)` | `=sqrt((2K_(max))/(m))\ \ `… (1) |
`r=(mv)/(qB)`
Substitute into (1):
`r=(m)/(qB)sqrt((2K_(max))/(m))`
`r prop sqrt(K_(max))`
When the photon energy is `2phi, K_max=phi.`
When the photon energy is doubled to `4phi, K_max=3phi.`
∴ As `r prop sqrt(K_(max)) ` the radius increases by a factor of `sqrt(3).`
`=>D`