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Fundamentals Of Physics
Found in: Page 91

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Short Answer

A magnetic field forces an electron to move in a circle with radial acceleration 3.0×1014m/s2 in a particular magnetic field. (a) What is the speed of the electron if the radius of its circular path is 15cm? (b)What is the period of the motion?

a) Speed of the electron is 6.7×106m/s.

b) Period of motion is1.4×10-7s.

See the step by step solution

Step by Step Solution

Step 1: Given

1) Radial acceleration, a=3×1014m/s2

2) Radius of the circular path,

r=15cm =0.15m

Step 2: Understanding the concept of centripetal acceleration

The centripetal acceleration of the object depends on the velocity and radius of the orbit. Using the equation of centripetal acceleration, we can calculate the speed of an electron moving in a circular direction. Using the value of the speed of an electron and the equation of period, we can find the period of motion of an electron.


a=V2r …(i)

T=2πrV …(ii)

Step 3: (a) Calculate the speed of the electron if the radius of its circular path is 15cm

From equation (i), we can write,


By rearranging this equation, we get,

v=ar =3×1014m/s2×0.15m =6.7×106m/s

Therefore, the speed of electron is6.7×106m/s .

Step 4: (b) Calculate the period of the motion

From equation (ii), we can write


Substitute the value of given radius and speed calculated in part (a), we get

T=2π×0.15m6.7×106m/s =1.4×10-7s

Therefore, the time period of rotation of electron is 1.4×10-7s.

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