- #1
jhosamelly
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Homework Statement
Find the magnitude and direction of the magnetic force on a charged particle with charge -4nC and velocity
[itex]\vec{v}[/itex] = [itex] (2.5\times 10^{4}) \hat{i}[/itex] + [itex] (1.1 \times 10^{4}) \hat{j}[/itex] (m/s)
if the magnetic field in the region is given by
[itex]\vec{B}[/itex] = [itex](1.2\times 10^{-3}) \hat{i}[/itex] + [itex](5.6 \times 10^{-3}) \hat{j}[/itex] - [itex](3.2 \times 10^{-3}) \hat{k}[/itex] (T).
Homework Equations
[itex]\vec{F}[/itex] = q ([itex]\vec{v}[/itex] [itex]\times[/itex] [itex]\vec{B}[/itex])
The Attempt at a Solution
[itex]\vec{F}[/itex] = q ([itex]\vec{v}[/itex] [itex]\times[/itex] [itex]\vec{B}[/itex])
[itex]\vec{F}[/itex] = ([itex] -4 \times 10^{-9} C [/itex]) [itex] \left[\left((2.5\times 10^{4}) \hat{i} + (1.1 \times 10^{4}) \hat{j}\right) \times \left((1.2\times 10^{-3}) \hat{i} + (5.6 \times 10^{-3}) \hat{j} - (3.2 \times 10^{-3}) \hat{k} \right) \right][/itex]
[itex]\vec{F}[/itex] = ([itex] -4 \times 10^{-9} C [/itex])[itex] \left[\left[(1.1 \times 10^{4})(-3.2 \times 10^{-3})\right] \hat{i} - \left[(2.5 \times 10^{4})(-3.2 \times 10^{-3})\right] \hat{j}+ \left[(2.5 \times 10^{4})(5.6 \times 10^{-3}) - (1.1 \times 10^{4}) (1.2 \times 10^{-3})\right] \hat{k}\right] [/itex]
[itex]\vec{F}[/itex] = ([itex] -4 \times 10^{-9} C [/itex]) ([itex]-35.2 \hat{i} + 80 \hat{j} + 126.8 \hat{k} [/itex])
[itex]\vec{F}[/itex] = [itex] (1.4 \times 10^{-7}) \hat{i}[/itex] - [itex] (3.2 \times 10^{-7}) \hat{j} - (5.0 \times 10^{-7})\hat{k} [/itex] (N)
Is this already the answer? Am I correct? Thanks in advance.
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