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An electron of mass m (9.1 times 10-31 kg) and charge q (-1.6 times 10-19 C) is accelerated to the right (in the plane of the page) from rest through a potential difference V = 1500 V. The electron then enters a region, defined by x > 0, containing a uniform magnetic field B = 0.3 T directed out of page. How much time, T (in seconds), does the electron spend in the magnetic field region?

Respuesta :

Answer:

The time is [tex]6.07\times10^{-34}\ sec[/tex]

Explanation:

Given that,

Mass of electron [tex]m=9.1\times10^{-31}\ kg[/tex]

Charge of electron [tex]e=-1.6\times10^{-19}\ C[/tex]

Potential difference = 1500 V

Magnetic field = 0.3 T

We need to calculate the speed of electron

Using formula of force

[tex]F_{m}=F_{e}[/tex]

[tex]qvB=eV[/tex]

[tex]v=\dfrac{eV}{qB}[/tex]

[tex]v=\dfrac{1.6\times10^{-19}\times1500}{1.6\times10^{-19}\times0.3}[/tex]

[tex]v=5000\ m/s[/tex]

We need to calculate the time

Using centripetal force

[tex]\dfrac{mv^2}{r}=qvB[/tex]

[tex]\dfrac{r}{v}=\dfrac{m}{qB}[/tex]

Put the value into the formula

[tex]t=\dfrac{9.1\times10^{-31}}{5000\times0.3}[/tex]

[tex]t=6.07\times10^{-34}\ sec[/tex]

Hence, The time is [tex]6.07\times10^{-34}\ sec[/tex]

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