n.b: The following is all math problems, dealing with vectors, I just need someone to check i'm doing the cross products and dot products properly< thank you! :)(adsbygoogle = window.adsbygoogle || []).push({});

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The electric field exerts a force per unit charge:

[tex] \bf{E} = (\hat{x} - 2\hat{y} + 4\hat{z}). [/tex]

i) What is the magnitude of E?

ii) What angle the E make with the Z axis (polar angle)

iii) What angle does the projection of the vector on the xy plane make with the x-axis (azimuthal angle)?

iv) The electric field displaces a charge by, [tex] \bf{d} = (2\hat{x} - \hat{y} + 6\hat{z})[/tex]m, Find the work done per unit charge by the electric field?

v) The electric field in iv is applied at the point [tex] P = (1,2,0) [/tex] m. What is the torque about the origin on a unit charge placed at P?

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relevant equations:

Work done per unit of charge = [tex] \bf{E.d} [/tex]

Torque on a unit charge, [tex]\bf{\tau = r x E}[/tex]

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my attempt:

i) magnitude of E is just the sum of the square of the components,

x^2 - 2y^2 + 4z^2 = 1^2 -2^2 + 4^2 = 1 +4 + 16 = 21

[tex] | E | = sqrt{21} [/tex]

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ii) what angle does it make with the z axis?

I managed to get 90-arcsin(4/|e|) = 45 degrees

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iii)What angle does the projection make with the x axis,

I had, arccos(1/(sqrt(5)) = 27.5 degrees

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iv)

the dot product of

[tex] \bf{E} = (\hat{x} - 2\hat{y} + 4\hat{z}). [/tex]

and [tex] \bf{d} = (2\hat{x} - \hat{y} + 6\hat{z})[/tex]

(1,-2,4) . (2,-1,6) = 2 + 2 +24 = 28,

I know the units of E = vm^-1 and the displacment vector d is m

what happens when I dot product that? It should be joules, since it is the work done, but i don't understand how to form that from those two unit types

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v)

the torque is the cross product of r x E

[tex] P = (1,2,0) [/tex] (which I think is r?)

[tex] \bf{E} = (\hat{x} - 2\hat{y} + 4\hat{z}). [/tex]

2 0 1 2

-2 4 1 -2

=

(8,-4,-4)

making the torque vector

[tex] \bf{\tau} = (8\hat{x} -4\hat{y} -4\hat{z} [/tex]

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thank you for checking

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# Homework Help: Electromagnetism Vectors

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