Question

A velocity selector has a magnetic field of magnitude 0.22 T perpendicular to an electric field of magnitude 0.51 MV/m.

Answer 1

Answer:

speed of a particle  = 2.31 × $10^{6}$ m/s

energy of proton required = 27.77 KeV

energy of electron required =  15.171 eV

Explanation:

given data

magnetic field of magnitude = 0.22 T

electric field of magnitude = 0.51 MV/m

to find out

speed of a particle and energy must protons have to pass through undeflected and  energy must electrons have to pass through undeflected

solution

we know that force due to magnetic and electric field is express as

force due to magnetic field B = qvB    ..............1

and force due to electric field E = qE   .....................2

so without deflection force due to magnetic field  = force due to electric field  

so here qvB = qE

and V = $\frac{E}{B}$    ...................3

put here value

V =  $\frac{0.51*10^6}{0.22}$

speed of a particle  = 2.31 × $10^{6}$ m/s

and

now energy of proton required will be here as

energy of proton required = mass of proton × $\frac{V^2}{2}$

put here value

energy of proton required = 1.67 × $10^{-27}$ × $\frac{(2.31*10^6)^2}{2}$

energy of proton required = 4.45 × $10^{-15}$ J

energy of proton required = 4.45 × $10^{-15}$ J ÷ (1.602 × $10^{-19}$

energy of proton required = 27777.777 eV

energy of proton required = 27.77 KeV

and

now we get here energy of electron required that is

energy of electron required = mass of electron × $\frac{V^2}{2}$

put here value

energy of electron required = 9.11 × $10^{-31}$ × $\frac{(2.31*10^6)^2}{2}$

energy of electron required =  24.305× $10^{-19}$ J

energy of electron required =  24.305 × $10^{-19}$ J ÷ (1.602 × $10^{-19}$  

energy of electron required =  15.171 eV

Answer 2

Answer:

Explanation:

magnetic field, B = 0.22 T

Electric field, E = 0.51 MV/m = 5100 V/m

(a) let the velocity is v.

v = E / B = 5100 / 0.22

v = 23181.82 m/s

(b) Energy of proton

E = 0.5 mv²

where, m is the mass of proton = 1.67 x 10^-27 kg

E = 0.5 x 1.67 x 10^-27 x 23181.82 x 23181.82

E = 4.48 x 10^-19 J

E = 2.8 eV  

(c) Energy of proton

E = 0.5 mv²

where, m is the mass of electron = 9.1 x 10^-31 kg

E = 0.5 x 9.1 x 10^-31 x 23181.82 x 23181.82

E = 2.445 x 10^-22 J

E = 1.53 x 10^-3 eV