An electron at point a has a speed v0 of 1.41x106 m/s. find (a) the magnitude and direction of the magnetic field that will cause the electron to follow a semi circular path from a to b, and

(a). The magnitude of the magnetic field is

(b). The time required for the electron to move from A to B is .

(c). The magnetic field is 0.2943 T.

Explanation:

Given that,

Speed

We need to calculate the magnetic field

Using formula of magnetic force and centripetal force

Where, m = mass of electron

v = speed of electron

q = charge of electron

r = radius of circular path

Put the value into the formula

The direction of the magnetic field must be into the page by the right hand and curls finger rule.

(b).  The time required for the electron to move from A to B will be given as :

We need to calculate the time

Using formula of time

Where, d =  total distance traveled by an electron

v = speed of electron

Put the value into the formula

The time required for the electron to move from A to B is .

(c). If the particle were a proton instead of an electron

We need to calculate the magnetic field

Using formula of magnetic field

Put the value into the formula

The magnetic field is 0.2943 T.

Hence, (a). The magnitude of the magnetic field is

(b). The time required for the electron to move from A to B is .

(c). The magnetic field is 0.2943 T.

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