In the following vector quantities are shown in bold and scalars in italics. The

Question

In the following vector quantities are shown in bold and scalars in italics. The electric field exerts a force per unit charge. An electric field is given by E = (2x - y + 6z). What is the magnitude of E? What angle does it make with the z-axis (polar angle)? What angle does the projection of the vector on the xy plane make with the x-axis (azimuthal angle)? The electric field displaces a charge by d = (x - 2y + 4z)m. Find the work done per unit charge by the electric field? [Work done per unit charge = E middot d] The electric field in (iv) is applied at the point P = (2, 1, 0) m. What is the torque about the origin on a unit charge placed at P? [Torque on a unit charge, tau = r times E].

Explanation / Answer

Here ,

E = 2x - y + 6 z

i) magnitude of E = sqrt(2^2 + 1^2 + 6^2)

magnitude of E = 6.403 N/C

ii)

angle with z -axis = arccos(6/6.403)

angle with z -axis = 20.43 degree

iii)

Now , for the azimuthal angle

azimuthal angle = 90 - 20.43 degree

azimuthal angle = 69.6 degree

iv) work done by electric field = (2x - y + 6z).(x -2y + 4z)

work done by electric field = 2 + 2 + 24

work done by electric field = 28 J

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