How is the Force on Charge q Distributed Along the Rod?

In summary, the charge Q = 1.95e-04 C is distributed uniformly along a rod of length 2L, and a charge q = 2.45e-06 C, with the same sign as Q, is placed at (D,0) where D = 60.0 cm. The net force on q in the y-direction is zero due to symmetry. Statement A is false because the correct equation for the force on q due to the segment dy is dF=(kqQ/4L^2*r^2)dy. Statement B is true because the net force on q in the x-direction is generally in the east direction. Statement C is false because the net force on q in the
  • #1
GingerBread27
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0
A charge Q = 1.95e-04 C is distributed uniformly along a rod of length 2L, extending from y = -14.2 cm to y = +14.2 cm, as shown in the diagram on your assignment. A charge q = 2.45e-06 C, and the same sign as Q, is placed at (D,0), where D = 60.0 cm.
Consider the situation as described above and the following statements. If the statement is true, answer T, if it is false, answer F, and if the answer cannot be determined from the information provided, answer C. For example if B and C are true and there is not enough information to answer D and the rest are false, then answer FTTCF.

A)The magnitude of the force on charge q due to the small segment dy is dF=(kqQ/16L*Lr*r)dy
B)The total force on q is generally in the east direction.
C)The net force on q in the x-direction equals zero.
D)The charge on a segment of the rod of infinitesimal length dy is given by dQ=(Q/4L*L)dy
E)The net force on q in the y-direction does equal zero.

Now I keep getting this wrong and I don't know why. As far as answers the only one I'm pretty sure about is that E is true because by symmetry the y components will cancel out. I put A is false because I'm not sure where the 16 is coming from. I put B as uncertain because you really can't be sure where the force is going and for D I put false because I get that dQ=Q/2L. We just started covering this material so I'm very lost.

A second question asks to : Use integration to compute the total force on q in the x-direction (in N). I know I haveto take the integral from one of the rod to the other but not sure what equation to integrate. Please help.
 

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  • #2
E is okay,and the reasoning is good.Which means that the total force in D (the point) is along the x axis,pointing E (eastwards).This means that the answer C is false and B is correct (net force=total force=resulting force).

Think about A and D.They are related.

Daniel.
 
  • #3
Ok figured out A and D were false now I'm lost as to how to answer the second part of the question about the force on q in x-direction.
 
  • #4
Compute the elementary force the infinitesimal length "dy" acts on the charge "q" at "D".

Use geometry to find this force...

Integrate from -L->+L to find the total force...

Daniel.
 

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Electricity is a form of energy caused by the movement of electrons. It can be produced by a variety of sources, including chemical reactions, mechanical energy, and solar energy.

2. How does electricity create force?

Electricity creates force through the interaction between charged particles. When two objects with opposite charges are brought close together, they will attract each other, creating a force. This force is known as electrostatic force.

3. What is the relationship between electricity and magnetism?

Electricity and magnetism are closely related and are actually different aspects of the same force, known as electromagnetism. Moving electric charges create magnetic fields, and changing magnetic fields can create electric currents.

4. What is the difference between AC and DC electricity?

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