Extra Credit: Show all your work to obtain credit. A beam of alpha particles ( q = +2e, mass = 6.64 x 10-27 kg) is accelerated from rest through a potential difference of 1.8 kV. The beam is then entered into a region between two parallel metal plates with potential difference 120 V and a separation 8 mm, perpendicular to the direction of the field. What magnitude of magnetic field is needed so that the alpha particles emerge undeflected from between the plates?

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Chrisnando Chrisnando · Answer 1 · 2020-05-06T11:31:12+02:00

Answer:

B = 0.036 T

Explanation:

Given:

[tex]m = 6.64*10^-^2^7[/tex]

p.d, Va= 1.8 KV = 1800V

Distance btw plates, d= 8mm = 0.008m

[tex]q = 2 * 1.6*10^-^1^9[/tex]

Let's use the equation:

[tex] q*Va = \frac{1}{2} mv^2 [/tex]

Substitute figures in the equation, we have:

[tex] 2*1.6*10^-^1^9 * 1800 = \frac{1}{2} * 6.64*10^-^2^7 * v'^2 [/tex]

Solving for v' we have:

[tex] v' = 41.65 * 10^4 [/tex]

For electric field between plates, we use the formula :

[tex] E = \frac{V}{d} [/tex]

Where V = 120

[tex] E = \frac{120}{0.008} [/tex]

[tex] 15*10^3 N/C [/tex]

The magnitude of magnetic field, B, needed so that the alpha particles emerge undeflected will be given as:

[tex] B = \frac{E}{v'} [/tex]

[tex] B = \frac{15*10^3}{41.65*10^4} [/tex]

B = 0.036 T