A monoenergetic (18 keV) electron beam initially in the horizontal direction is subjected to a horizontal magnetic field of 0.40 G normal to the initial direction. Estimate the up or down deflection of the beam over a distance of 30 cm. Given mass of electron 9.11 x 10^–31 kg and charge on electron = 1.6 x 10^–19 C.
[Note: Data in this exercise are so chosen that the answer will give you an idea of the effect of earth’s magnetic field on the motion of electron beam from electron gun to the screen in a T.V. set.]

Solution

Here,
Energy of the electron beam, E = 18 keV = $18 \times 1.6 \times 10^{- 16} J$
Horizontal magnetic field, B = 0.40 G = 0.40 $\times$ $10^{- 4} T$
distnace, $x = 30 cm = 0.3 m$

As,
Energy, $E = \frac{1}{2} m v^{2}$

$∴ v = \sqrt{2 E / m}$

In a magnetic field, electron beam is deflected along a circular arc of radius r, such that
$Beν = \frac{{mν}^{2}}{r} \Rightarrow r = \frac{mv}{Be} r = \frac{m}{Be} \sqrt{\frac{2 E}{m}} = \frac{1}{Be} \sqrt{2 E m} = 11.3 m$

In $△ OCB,$

$\sin θ = \frac{x}{r}$
$\sin θ = \frac{0.3}{11.3} = \frac{3}{113}$

$y = r - OC = r - r \cos θ = r (1 - \cos θ) = r [1 - \sqrt{1 - \sin^{2} θ}]$

By using binomial expansion,
$y = r [1 - (1 - \frac{1}{2} \sin^{2} θ)] y = \frac{r}{2} . \sin^{2} θ y = \frac{11.3}{2} \times \frac{3 \times 3}{113 \times 113 \times 10} = \frac{9}{2260} = 3.98 \times 10^{- 3} ≅ 4 mm .$

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Magnetism And Matter

Some More Questions From Magnetism and Matter Chapter

Answer the following question regarding earth:
Geologists claim that besides the main magnetic N-S poles, there are several local poles on the earth's surface oriented in different directions. How is such a thing possible at all?

Answer the following question:
The earth's magnetic field varies from point to point in space. Does it also change with time? If so, on what time scale does it change appreciably?

Answer the following question:
The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism. Why?

Answer the following question:
The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism. What might be the ‘battery’ (i.e., the source of energy) to sustain these currents?

Answer the following question:
The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past?

Answer the following question:
The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?

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For Daily Free Study Material Join wiredfaculty

Magnetism And Matter

Some More Questions From Magnetism and Matter Chapter

Answer the following question regarding earth:Geologists claim that besides the main magnetic N-S poles, there are several local poles on the earth's surface oriented in different directions. How is such a thing possible at all?

Answer the following question:The earth's magnetic field varies from point to point in space. Does it also change with time? If so, on what time scale does it change appreciably?

Answer the following question:The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism. Why?

Answer the following question:The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism. What might be the ‘battery’ (i.e., the source of energy) to sustain these currents?

Answer the following question:The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past?

Answer the following question:The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Answer the following question regarding earth:
Geologists claim that besides the main magnetic N-S poles, there are several local poles on the earth's surface oriented in different directions. How is such a thing possible at all?

Answer the following question:
The earth's magnetic field varies from point to point in space. Does it also change with time? If so, on what time scale does it change appreciably?

Answer the following question:
The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism. Why?

Answer the following question:
The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism. What might be the ‘battery’ (i.e., the source of energy) to sustain these currents?

Answer the following question:
The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past?

Answer the following question:
The earth’s field departs from its dipole shape substantially at large distances (greater than about 30,000 km). What agencies may be responsible for this distortion?