Question

pic A proton (mass= 1.67×10-27 kg, charge= 1.6×10-19 C) travelling with speed 1×106 m/s enters a region of space containing a uniform magnetic field of 1.2 T. What is the time t required for the proton to re-emerge into the field-free region? t =

Answer 1

Complete Question

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Answer:

The time t required is
`t= 2.73 *10^(-8) sec`

Step-by-step explanation:

When this proton move into the magnetic field region the magnetic field would cause it to move in a clockwise direction

The force which it would feel inside the field is mathematically denoted as follows

`F = qvB`

And this is the same thing as the force which keeps it around the circle without spiraling off and this is also know as centripetal force and it is mathematically

`F_c = (mv^2)/(r)`

Since the two force are equal we can equate the formulas

`qvB = (mv^2)/(r)`

making r the subject of the formula

`r = (mv)/(qB) = ((1.67*10^(-27)(1*10^6)))/((1.60*10^(-19)(1.2))) = 8.7*10^(-3) m`

Now mathematically the total distance traveled is

`S = \pi r`

Since
`Time = (distance )/(velocity)`

=
`(\pi r)/(v) =((3.142 *8.7*10^(-3)))/(1*10^6) = 2.73 *10^(-8) sec`