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An electron that has a velocity with x component 1.6 × 10^6 m/s and y component 2.6 × 10^6 m/s moves through a uniform magnetic field with x component 0.024 T and y component -0.14 T. (a) Find the magnitude of the magnetic force on the electron. (b) Repeat your calculation for a proton having the same velocity.

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Answer:

(a)

[tex]\overrightarrow{F}=4.58\times10^{-14}\widehat{K}N[/tex]

(b) [tex]\overrightarrow{F}=- 4.58\times10^{-14}\widehat{K}N[/tex]

Explanation:

Vx = 1.6 x 10^6 m/s

Vy = 2.6 x 10^6 m/s

Bx = 0.024 T

By = - 0.14 T

charge of electron, q = - 1.6 x 10^-19 C

charge of proton, q = 1.6 x 10^-19 C

(a) Force on electron is given by

[tex]\overrightarrow{F}=q(\overrightarrow{V}\times \overrightarrow{B})[/tex]

Substituting the values

[tex]\overrightarrow{F}=-1.6\times10^{-19}{\left ( 1.6\times 10^{6}\widehat{i}+2.6 \times 10^{6}\widehat{j} \right )\times \left ( 0.024\widehat{i}-0.14\widehat{j} \right )}[/tex]

[tex]\overrightarrow{F}=4.58\times10^{-14}\widehat{K}N[/tex]

(b) Force on proton is given by

[tex]\overrightarrow{F}=q(\overrightarrow{V}\times \overrightarrow{B})[/tex]

Substituting the values

[tex]\overrightarrow{F}=1.6\times10^{-19}{\left ( 1.6\times 10^{6}\widehat{i}+2.6 \times 10^{6}\widehat{j} \right )\times \left ( 0.024\widehat{i}-0.14\widehat{j} \right )}[/tex]

[tex]\overrightarrow{F}=- 4.58\times10^{-14}\widehat{K}N[/tex]

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