What Is the Net Dipole Moment of This Three-Point Charge Distribution?

[vrinda mukund]

Homework Statement

three point charges q,q and -2q are located at (0,-a,a), (0,a,a) and (0,0,-a) respectively. what is the net dipole moment of these charge distribution.?

Homework Equations

moment p =qd.

The Attempt at a Solution

Here we have to consider only the yz plane as x is always 0. when draw we can see the arrangement as three charges situated at the corners of a triangle. buy how can these charges form a dipole. in a dipole charges should be equal and opposite, rite? but none of the pairs formed between these three charges satisfies that requirement. how to solve this problem? help me please

 

[ehild]

Consider the -2q charge as two -q charges at the same place. This way, you have two dipoles, one with q charge at (0,-a,a) and -q at (0,0,-a), the other one with q at (0,a,a) and -q at (0,0,-a). Do not forget that the dipole moment is a vector, it points from the negative charge to the positive one. Add them as vectors. ehild

 

[vrinda mukund]

Thank u sir for ur guidance. now i understood how they form a dipole. but still i am not getting the answer. by calculating in the way that u said i got that length of each dipole is (a*square root of 5) and dipole = (q*a*square root of 5). then the resultant dipole should be along Z axis, i.e. along k hat direction and total magnitude should be 2(q*a*square root of 5). but the four options given for the question does not include this result.

 

[ehild]

The dipoles are vectors, their components add instead of the lengths. The dipoles in this problem are p1=q(0,-a,2a) and p2=q(0,a,2a) What is their sum?

ehild

 

[vrinda mukund]

thank u sir,i got the answer as 4QA(k hat).
but sir i again got confused with another problem of very similar type. in this case the charges are placed at the corners of a square. Q at (0,0,0), Q at (a,0,0), -2Q at(a,a,0) and Q at (0,a,0). in this case also i think there are only two dipole. considering the -2Q charge at (a,a,0) as two -Q charges we have two dipoles, one between -Q charge at (a,a,0) and Q at (a,0,0) and the second dipole between the other -Q charge at (a,a,0) and Q at (0,a,0).

in this case i got the answer as -qa(i hat)-qa(j hat). but my friend was saying that answer will be qa(i hat)+qa(j hat) . which is the right answer?

 

[ehild]

The dipole moment is a vector, that points from the negative charge to the positive one.

ehild