An electron entering Thomson’s e/m apparatus has an initial speed (in the horizontal direction only) of 4.0 ×106 /. In the lab is a permanent horseshoe magnet of strength 12 , which you would like to use. (a) What electric field will you need in order to produce zero deflection of the electrons as they travel through the apparatus?
(b) The length of nonzero electric and magnetic fields is 2.0 . When the magnetic field is turned off, but the same electric field remains, how far in the vertical direction will the electron beam be deflected over this length?

c) up

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we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .