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- Homework Statement
- An electron with velocity v =##2 \times 10^6 \\ \mathrm {ms^-1}##

enters a square region ABCD (of area a = ##1 \\ \mathrm cm^2##

along one of its side AB. Inside the region there is a magnetic field B perpendicular to the

area of the square. Find the minimum value of magnetic field for which the electron will

come out of the square with a velocity parallel to its initial velocity(parallel doesn't

necessarily mean in the same direction).

- Relevant Equations
- ##\vec B = \frac{\mu_0 q \vec v\times \hat r}{4\pi r^2}##

When I try following numbers from internet then I don't get an expected answer.

## \mu_0 = 1.25663706 × 10-6 m kg s^{-2} A^{-2}##

##q =1.60217662 × 10^{-19} coulombs ##

##r=2.82x10^{-15} m##

Velocity of that electron is given in question

##\vec v= 2 \times 10^6 \\ \mathrm{ms^{-1}}##

Since magnetic field is perpendicular to the surface that's why I took ##\vec v \times \hat r=||v||## Wait a minute, Magnetic field is perpendicular but not velocity and velocity is parallel so ##\vec v \times \hat r=0##. But if I tried it then I would get "nothing". Did I take wrong equation? Or there's some concept which I haven't figured out?

## \mu_0 = 1.25663706 × 10-6 m kg s^{-2} A^{-2}##

##q =1.60217662 × 10^{-19} coulombs ##

##r=2.82x10^{-15} m##

Velocity of that electron is given in question

##\vec v= 2 \times 10^6 \\ \mathrm{ms^{-1}}##

Since magnetic field is perpendicular to the surface that's why I took ##\vec v \times \hat r=||v||## Wait a minute, Magnetic field is perpendicular but not velocity and velocity is parallel so ##\vec v \times \hat r=0##. But if I tried it then I would get "nothing". Did I take wrong equation? Or there's some concept which I haven't figured out?

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