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If you live in Melbourne, Australia, the local magnetic field has a strength of about 4x10-5 T. The magnetic field vector is directed northward, making an angle of 30 deg above the horizontal. An electron in Melbourne is moving parallel to the ground, in the west direction, at a speed of 9x105 m/s. What are the magnitude and direction of the magnetic force on the electron

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Answer:

[tex]5.76\times 10^{-18}\ \text{N}[/tex] perpendicular to the velocity and magnetic field

Explanation:

B = Magnetic field = [tex]4\times 10^{-5}\ \text{T}[/tex]

[tex]\theta[/tex] = Angle the magnetic field makes with the horizontal = [tex]30^{\circ}[/tex]

v = Velocity of electron = [tex]9\times 10^5\ \text{m/s}[/tex]

q = Charge of electron = [tex]1.6\times 10^{-19}\ \text{C}[/tex]

Magnetic force is given by

[tex]F=qvB\sin\theta\\\Rightarrow F=1.6\times 10^{-19}\times 9\times 10^5\times 4\times 10^{-5}\sin30^{\circ}\\\Rightarrow F=2.88\times 10^{-18}\ \text{N}[/tex]

The magnitude of the magnetic force is [tex]2.88\times 10^{-18}\ \text{N}[/tex] and the direction is perpendicular to the velocity and magnetic field.

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