Question

# An electron with a velocity given by v⃗ =(1.6×105 m/s )x^+(6700 m/s )y^ moves through a...

An electron with a velocity given by v⃗ =(1.6×105 m/s )x^+(6700 m/s )y^ moves through a region of space with a magnetic field B⃗ ==(0.26 T )x^−(0.10 T )z^ and an electric field E⃗ =(220 N/C )x^.

Using cross products, find the magnitude of the net force acting on the electron. (Cross products are discussed in Appendix A.)

Net force on electron due to magnetic and electric field will be:

F_net = Fe + Fm

Fe = Force due to electric field = q*E

Fm = Force due to magnetic field = q*(VxB)

q = charge on electron = -1.6*10^-19 C

E = Electric field = (220 N/C) x^ = 220 i

Using x^ = i, y^ = j, z^ = k

V = (1.6*10^5 i + 6700 j) m/s

B = (0.26 i - 0.10 k) T

So,

So,

F_net = q*E + q*(VXB) = q*[E + VxB]

F_net = -1.6*10^-19*[220 i - 670 i + 1.6*10^4 j - 1742 k]

F_net = 1.6*10^-19*450 i - 1.6*1.6*10^-15 j + 1.6*10^-19*1742 k

F_net = 7.2*10^-17 i - 2.56*10^-15 j + 2.787*10^-16 k

In two significant figures:

F_net = 7.2*10^-17 i - 2.6*10^-15 j + 2.8*10^-16 k

F_net = (7.2*10^-17 N) x^ - (260*10^-17 N) y^ + (28*10^-17 N) z^

Let me know if you've any query.

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