Respuesta :
Answer:
B = 0.0429 T
Explanation:
It is given that,
Voltage of battery, V = 150 V
Area of two plates, [tex]A=28.5\ cm^2=0.00285\ m^2[/tex]
Separation between the plates, d = 8.5 mm = 0.0085 m
Charge on alpha particles, q = 2e
Mass of alpha particle, [tex]m=6.64\times 10^{-27}\ kg[/tex]
It is accelerated from rest through a potential difference of 1.75 kV and enters the region between the plates perpendicular to the electric field.
Firstly using the conservation of energy as :
[tex]\dfrac{1}{2}mv^2=qV[/tex]
[tex]v=\sqrt{\dfrac{2qV}{m}}[/tex]
[tex]v=\sqrt{\dfrac{2\times 2\times 1.6\times 10^{-19}\times 1.75\times 10^{3}}{6.64\times 10^{-27}}}[/tex]
v = 410700.25 m/s
As the alpha particle goes undeflected, the magnetic force is equal to the magnetic force as :
[tex]qvB=qE[/tex]
[tex]B=\dfrac{E}{v}[/tex]
E is the electric field, [tex]E=\dfrac{V}{d}[/tex]
[tex]B=\dfrac{V}{v\times d}[/tex]
[tex]B=\dfrac{150}{410700.25\times 0.0085}[/tex]
B = 0.0429 T
So, the magnetic field is needed so that the alpha particles emerge undeflected from between the plates is 0.0429 T. Hence, this is the required solution.
The magnitude of magnetic field needed so that the alpha particles emerge undeflected from between the plate is 0.043 Tesla
The parameter given are:
Voltage of battery, V = 150 V
Plates area A = 28.5 cm^2
Distance between the plates, d = 8.5 mm = 0.0085 m
Charge on the particles, q = 2e = 2 x 1.6 x 10^-19
q = 3.2 x 10^-19
Particle mass M = 6.64 x 10^-27
potential difference = 1.75 kV
From conservation of energy, the total kinetic energy of the accelerated particle is equal to the electric potential of the particle. That is,
1/2mv^2 = qV
mv^2 = 2qV
v^2 = 2qV/m
v = [tex]\sqrt{2qV/m}[/tex]
v = [tex]\sqrt{(2*3.2*10^-19 * 1.75 * 1000)/6.64 * 10^-27}[/tex]
v = [tex]\sqrt{1.6*10^11}[/tex]
v = 410,700.25 m/s
Since the alpha particle goes undeflected, the magnetic force will be equal to the electric force. That is,
Bvq = qE
Where E = Electric field
Make the magnetic field B the subject of the formula
B = qE/vq
B = E/v
But E the electric field = V/d
Therefore,
B = V/dv
B = 150/(0.0085 x 410700.25)
B = 0.0429
B = 0.043 approximately
Therefore, the magnetic field needed for the alpha particles to emerge undeflected between the plates is 0.043 Tesla
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