(10%) Problem 7: In a mass spectrometer, a specific velocity can be selected from a distribution by injecting charged particles between a set of plates with a constant electric field between them and a magnetic field across them (perpendicular to the direction of particle travel). If the fields are tuned exactly right, only particles of a specific velocity will pass through this region undeflected. Consider such a velocity selector in a mass spectrometer with a 0.095 T magnetic field.
What electric field strength, in volts per meter, is needed to select a speed of 4.1 x 10^6 ms?
Answer:
The strength of electric field is [tex]3.9 \times 10^{5}[/tex] [tex]\frac{V}{m}[/tex]
Explanation:
Given:
Magnetic field [tex]B = 0.095[/tex] T
Speed of particle [tex]v = 4.1 \times 10^{6}[/tex] [tex]\frac{m}{s}[/tex]
Here we equate two forces
[tex]F_{E} = F_{B}[/tex]
[tex]qE = qvB[/tex]
[tex]E = vB[/tex]
For finding electric field strength,
[tex]E = 4.1 \times 10^{6} \times 0.095[/tex]
[tex]E = 3.9 \times 10^{}[/tex] [tex]\frac{V}{m}[/tex]
Therefore, the strength of electric field is [tex]3.9 \times 10^{5}[/tex] [tex]\frac{V}{m}[/tex]