Consider two vectors: E1 with magnitude 7 N/C and at an angle of 20 degrees above the positive x direction, and E2 with magnitude 5 N/C and at an angle of 30 degrees to the left of the positive y direction. (a) Visualizing vector sums: Draw a vector sum diagram illustrating the sum EN = E1 + E2 and another of the vector difference E1 = EN − E2. Make sure to label your arrows. Please make the diagram as close to scale as possible (use a ruler to measure, or use a program that lets you draw accurately.) (b) Interpreting vector diagrams: From the diagram, should the magnitude of the sum be larger or smaller than 7 N/C? From the diagram, predict the general direction of the sum, within 1/8 of a circle (for instance, between 0 and 45 degrees above the x axis, etc.) Note, this is one good way to check your own answers when working with vectors. (c) Calculating vector components and sums: Compute the components and then the magnitude and direction of the sum. For direction, we want the angle between the x axis and the sum vector. Compare the length of the sum arrow in part (a) to your calculated magnitude, taking into account the scale of your drawing. Compare the calculated angle and the predicted direction. Are your quantitative answers consistent with your diagrams? (d) Multiplying vectors by scalars: The force on a test charge Q by a field E is given by F = QE. Use this to find the components, magnitude and direction of the force F1 by EN on a negative charge Q1 = −0.001C, and of the force F2 by EN on a positive charge Q2 = 0.002C. Do this in the most efficient way that requires the least amount of calculation! (e) Understanding unit vectors: Let’s get that unit vector business cleared up. The unit vector is a length one vector in the direction of some vector. Its components can be found by taking the original vector and dividing by that original vector’s magnitude. Calculate the components of the unit vector in the direction of EN , F1, and F2. Show that the magnitudes of all your unit vectors are one, with no units, and that the unit vectors for the forces do point in the same direction as the field for positive test charges and the opposite direction for negative charges.
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Consider two vectors: E1 with magnitude 7 N/C and at an angle of 20 degrees above the positive x
direction, and E2 with magnitude 5 N/C and at an angle of 30 degrees to the left of the positive y
direction.
(a) Visualizing vector sums: Draw a vector sum diagram illustrating the sum EN = E1 + E2 and
another of the vector difference E1 = EN − E2. Make sure to label your arrows. Please make
the diagram as close to scale as possible (use a ruler to measure, or use a program that lets you
draw accurately.)
(b) Interpreting vector diagrams: From the diagram, should the magnitude of the sum be larger or
smaller than 7 N/C? From the diagram, predict the general direction of the sum, within 1/8 of
a circle (for instance, between 0 and 45 degrees above the x axis, etc.) Note, this is one good
way to check your own answers when working with vectors.
(c) Calculating vector components and sums: Compute the components and then the magnitude and
direction of the sum. For direction, we want the angle between the x axis and the sum vector.
Compare the length of the sum arrow in part (a) to your calculated magnitude, taking into
account the scale of your drawing. Compare the calculated angle and the predicted direction.
Are your quantitative answers consistent with your diagrams?
(d) Multiplying vectors by scalars: The force on a test charge Q by a field E is given by F = QE.
Use this to find the components, magnitude and direction of the force F1 by EN on a negative
charge Q1 = −0.001C, and of the force F2 by EN on a positive charge Q2 = 0.002C. Do this in
the most efficient way that requires the least amount of calculation!
(e) Understanding unit vectors: Let’s get that unit vector business cleared up. The unit vector is
a length one vector in the direction of some vector. Its components can be found by taking the
original vector and dividing by that original vector’s magnitude.
Calculate the components of the unit vector in the direction of EN , F1, and F2. Show that
the magnitudes of all your unit vectors are one, with no units, and that the unit vectors for
the forces do point in the same direction as the field for positive test charges and the opposite
direction for negative charges.
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