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Q. 10 - Excercises And Problems

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

An electron in a cathode-ray beam passes between long parallel-plate electrodes that are apart. A

, 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 .

a. What is the electron’s speed?

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

(a) Speed of electron

(b) Electrons radius of curvature in magnetic field.

See the step by step solution

Step by Step Solution

Part(a) Step 1: Given information 

parallel plate electrode

length of electrode:

width(d): ;

magnetic field(B)= (perpendicular to electric field)

No deflection when

 Part(a) Step 2: Finding velocity of electron

Using formula:

When electron pass without deflection then (where v is speed of electron, E is electric field)

Hence, electron's speed is

Part(b) step 1: Given information 

parallel plate electrode

mass of electron(m)=

charge on electron(q)=

magnetic field(B)= (perpendicular to electric field)

velocity of electron=(from part (a))

Part(b) Step 2: Finding radius of curvature 

In presence of magnetic field only, we know that

where R is radius, m is mass of electron, v is its velocity, q is charge, B is magnetic field present;

Hence, electrons radius of curvature in magnetic field is

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