Question

An electron travels with speed $1.0\times {10}^7\mathrm{m}/\mathrm{s}$between the two parallel charged plates shown in FIGURE. The plates are separated by $1.0\mathrm{cm}$and are charged by a $200\mathrm{V}$battery. What magnetic field strength and direction will allow the electron to pass between the plates without being deflected?

Short answer

Magnetic field strength,$B=2\mathrm{mT}$ and its direction is into the page

Step-by-step solution

Field of force (part a) 

When a field of force is applied to the moving charges inside a conductor, the Hall-voltage is that the steady - state condition electrical difference between the $2$surfaces of the conductor. By equation, the Hall voltage is proportional to the present current $I$inside the conductor and also the flux.

$\Delta V_{\mathrm{H}}=w{v}_{\mathrm{d}}B$

Where $w$denotes the plate width. Because no magnetism is applied on the electron at the steady-state potential, the electron will tolerate the plates without deflection.

$B=\frac{\Delta V_{\mathrm{H}}}{w{v}_{\mathrm{d}}}$

Physical phenomenon (part b)

Put the values:

$B=\frac{\Delta V_{\mathrm{H}}}{w{v}_{\mathrm{d}}}$

$=\frac{200\mathrm{V}}{\left(1\times {10}^7\mathrm{m}/\mathrm{s}\right)(0.01\mathrm{m})}$

$=2\times {10}^{-3}\mathrm{T}$

$=2\mathrm{mT}$