Physics 230 Quiz 1

Write the following using symbols. Be precise!

- the
*y*-component of a vector**v** - The magnitude of the sum of two vectors
**v**_{1}and**v**_{2}

A point charge Q produces an electric field **E**_{1 }at point P of magnitude 5.0 N/C and direction 45^{◦} to the *x*-axis, as shown in the diagram. A second charge q produces an electric field **E**_{2 }at P of magnitude 8.0 N/C at 60^{◦}_{ }to the negative *x*-axis. What is the total electric field at point P?

The components of **E**_{1} are:

*x*-component: E_{1x} = (5 N/C)cos45 = (5 N/C)/√2 = 3.54 N/C

*y*-component: E_{1y} = (5 N/C)sin45 = (5 N/C)/√2 = 3.54 N/C

The components of **E**_{2} are:

*x*-component: E_{2x} = - (8 N/C)cos60 = - (8 N/C)/2 = -4.0 N/C

*y*-component: E_{2y} = (8 N/C)sin60 = (8 N/C)/√3/2 = 6.93 N/C

Adding then, we get

E_{x} = (3.54- 4) N/C = - 0.46 N/C rounds to - 0.5 N/C

and

E_{y} = (3.54 + 6.93) N/C = 10.46 N/C rounds to 10.5 N/C

We may also give the answer as **E **= √(0.5^{2} + 10.5^{2} ) N/C at tan^{-1}(10.5/.5) to the negative *x*-axis = 10.5 N/C at 87^{◦ } to the negative *x*-axis.