Electrons enter a region of perpendicular electric and magnetic fields. The regi

Question

Electrons enter a region of perpendicular electric and magnetic fields. The region occupied by the fields is40.0 mm long in the x direction, where x is taken to be the original direction of motion. After passing through this region, the electrons then travel an additional 300 mm in the x direction before hitting a phosphorescent screen that lights up where the electrons strike it. The electrons pass undeflected through the region of perpendicular fields whenE = 2.0 × 103 N/C and B = 1.5 × 105 T.(Figure 1) v=1.3 * 10^8 m.s

If the magnetic field is turned off but the electric field is left on, by what distance have the electrons been deflected when they reach the phosphorescent screen?

Explanation / Answer

given,

electric field = 2 * 10^3 N/C

region of field = 40 mm

additional distance covered = 300 mm

acceleration experienced by electron in electric field = qE/m

acceleration experienced by electron in electric field = 2 * 10^3 * 1.6 ^ 10^-19 / (9.109 * 10^-31)

acceleration experienced by electron in electric field = 3.51 * 10^14 m/s

time taken by electron to cover 40 mm = 40 * 10^-3 / (1.3 * 10^8)

time taken by electron to cover 40 mm = 3.07 * 10^-10 sec

vertical distance covered in this time

s = 0.5 * 3.51 * 10^14 * (3.07 * 10^-10)^2

s = 0.00001654069 m

final vertical velocity = 3.51 * 10^14 * (3.07 * 10^-10)

final vertical velocity = 107757 m/s

time taken by electron to cover 300 mm = 300 * 10^-3 / (1.3 * 10^8)

time taken by electron to cover 300 mm = 2.3 * 10^-9 sec

vertical distance covered = 2.3 * 10^-9 * 107757

vertical distance covered = 0.0002478411 m

total vertical distance covered = 0.00001654069 + 0.0002478411

total vertical distance covered = 0.00026438179 m

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