An electron in a cathode-ray beam passes between 2.5-cm-long parallel-plate elec

Question

An electron in a cathode-ray beam passes between 2.5-cm-long parallel-plate electrodes that are 5.2mm apart. A 2.4mT , 2.5-cm-wide magnetic field is perpendicular to the electric field between the plates. The electron passes through the electrodes without being deflected if the potential difference between the plates is 660V .

Part A

What is the electron's speed?

Express your answer to two significant figures and include the appropriate units

Part B

If the potential difference between the plates is set to zero, what is the electron's radius of curvature in the magnetic field?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

Electric field

E=V/d =660/(5.2*10-3)=1.27*105 N/C

speed of electron

v=E/B =(1.27*105)/(2.4*10-3)

v=5.3*107 m/s

b)

Centripetal force=Magnetic force

mv2/r=qvB

=>r=mv/qB =(9.11*10-31)(5.3*107)/(1.6*10-19)(2.4*10-3)

r=0.1255 m=0.13 m or 13 cm

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