First slide

Force on a charged particle moving in a magnetic field

Question

A uniform magnetic field with a slit system as shown in fig.is to be used as a momentum filter for high-energy charged particles' With a field Btesla' it is found that the filter transmits $α$ -particles each of energy 5 3 MeV. The magnetic field is increased to
2.3 B tesla and deuterons are passed into the filter' The energy of each deuteron transmitted by the filter is

Moderate

A

12 MeV
B

14MeV
C

16 MeV
D

20 MeV

Solution

Here $\frac{{mv}^{2}}{R} = qvB or mv = p = qBR$
so, Energy $E = \frac{p^{2}}{2 m} = \frac{q^{2} B^{2} R^{2}}{2 m}$
$E_{α} = \frac{4 e^{2} \times B^{2} \times R^{2}}{2 \times 4 m_{p}}, m_{p} = massofproton$
$\begin{array}{l} E_{d} = \frac{e^{2} \times (2 \cdot 3 B)^{2} \times R^{2}}{2 \times 2 m_{p}} \\ ∴ \frac{E_{d}}{E_{α}} = \frac{(2 \cdot 3)^{2}}{2} or \begin{array}{ll} E_{d} & = \frac{(2 \cdot 3)^{2} \times 5 \cdot 3}{2} \\ = 14 MeV \end{array} \end{array}$

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