Answer:
Magnetic field, [tex]B=2\times 10^{-4}\ T[/tex]
Explanation:
Given that,
Velocity of electron, [tex]v=5\times 10^7\ m/s[/tex]
It enters a region of space where perpendicular electric and a magnetic fields are present.
Magnitude of electric field, [tex]E=10^4\ V/m[/tex]
We need to find the magnetic field will allow the electron to go through the region without being deflected.
Magnetic force on the electron, [tex]F_m=qvB\ sin\theta[/tex].......(1)
Electric force on the electron, F = q E........(2)
From equation (1) and (2) we get:
[tex]qvB\ sin\theta=qE[/tex]
[tex]B=\dfrac{E}{v}[/tex]
[tex]B=\dfrac{10^4\ V/m}{5\times 10^7\ m/s}[/tex]
B = 0.0002 T
or
[tex]B=2\times 10^{-4}\ T[/tex]
Hence, this is the required solution.
