For detecting ions with mass numbers in the range 1 ≤ A M ≤ 196 , determine the minimum height ( x 1 − x 0 ) of the detector (in cm).

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PhysicsMagnetismMotion analysis in electric & magnetic fieldMedium3 minQB

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Passage / Comprehension

A positive, singly ionized atom of mass number $A_{M}$ is accelerated from rest by the voltage 192 V. Thereafter, it enters a rectangular region of width $w$ with magnetic field $B_{0} = 0.1 \hat{k}$ Tesla, as shown in the figure. The ion finally hits a detector at the distance x below its starting trajectory. [Given: Mass of neutron/proton $= (5/3) \times 1 0^{- 27} kg$ , charge of the electron $= 1.6 \times 1 0^{- 19} C$ .]\\

For detecting ions with mass numbers in the range $1 \leq A_{M} \leq 196$ , determine the minimum height $(x_{1} - x_{0})$ of the detector (in cm).

Answer:

52.00

Solution:

From Q3, $x = 2 r = (2/ B_{0}) 2 mV / e$ , so $x \propto A_{M}$ .

$A_{M} = 1 : x_{0} = 48/ 144 = 4 cm$ ; $A_{M} = 196 : x_{1} = 48 196/144 = 56 cm$ .

Minimum detector height $= x_{1} - x_{0} = 56 - 4 = 52 cm$ .

Stream:JEESubject:PhysicsTopic:MagnetismSubtopic:Motion analysis in electric & magnetic field

⏱ 3mℹ️ Source: QB

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