A +33.0 nC charge is placed at the origin of an xy-coordinate system, and a −25.0 nC charge is placed at the point (1.500 m, −0.0540 m).
(a) Determine the magnitude and the direction of the force that the positive charge exerts on the negative charge. Use ijk notation for your result.
ANS: -(3.29e-6)i +(1.18e-7)j N
That is the right answer, however I don't get the how they got the y position> i get 2.55e-3 .
Im not sure if i'm missing something, please help me out!
Thanks
F=l q1q2( r2-r1)/(r2-r1)^3
so , if the i is right, lets look only at the j component
Fj=kq1Q2(r2j-r1j)/( )^3
but r1 is the origin, so
r2=1.5i-.054j)
so the distance in the i is 1.5/.054= 27,7 times the j distance, so the force then should be 27.7 times less in that direction vector.
so, however you got the 3.29e-6, divide it by 27.7 to get 1.18e-7.
So this indicates you made a math error in computing the j direction only, probably calc error, all the other computes on the basic formula fraction are correct.
I don't quite understand why we had to do 1.5/.054 ? Like what is the reasoning behind it?
Why didn't we just do
F=(q1q2)/r^2
where r would now be 0.054? and if we can't do this why is it wrong to do this?
Really appreciate the help!
NO!
r = sqrt (1.5^2 + .054^2)
r^2 = 2.25+ .003 = 2.253
|F| = k q1 q2 /r^2
Fi = |F| cos angle above -xaxis
Fj = |F| sin angle above -x axis
that angle is tiny tan angle = .054/1.5
so cos angle is = 1
and sin angle = tan angle = .054/1.5
so
Fj = |F| * .054/1.5 = 1/27.7
as Bob Pursley was saying.
To calculate the magnitude and direction of the force exerted by the positive charge on the negative charge, you can use Coulomb's Law:
F = k * q1 * q2 / r^2
where F is the force, k is the Coulomb's constant (8.99e9 N m^2 / C^2), q1 and q2 are the charges, and r is the distance between the charges.
In this case, q1 = +33.0 nC = +33.0e-9 C and q2 = -25.0 nC = -25.0e-9 C. The distance between the charges, r, can be found using the distance formula:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates given (0, 0) for the positive charge and (1.500 m, -0.0540 m) for the negative charge, we can calculate the distance.
r = sqrt((1.500 m - 0)^2 + (-0.0540 m - 0)^2)
= sqrt(2.2500 m^2 + 0.002916 m^2)
= sqrt(2.252916 m^2)
= 1.501 m
Now, we can plug all these values into Coulomb's Law to find the force:
F = (8.99e9 N m^2 / C^2) * (+33.0e-9 C) * (-25.0e-9 C) / (1.501 m)^2
Calculating this expression gives:
F = -3.29e-6 N
So, the magnitude of the force is 3.29e-6 N. To find the direction, you need to express it in terms of the unit vectors i and j. The force is directed in the negative x-axis direction, which is why the x-component of the force is negative. The y-component of the force is positive, as it is directed along the positive y-axis.
Therefore, the answer is -(3.29e-6)i + (1.18e-7)j N, where i and j are the unit vectors along the x and y directions, respectively.