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Physics Help!
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A positive charge Q is on the y-axis at a distance a from the origin, and another positive charge q is on the x-axis at a distance b from the origin.
A) For what values(s) of b is the x-component of the force on q a minimum?
B) For what values(s) of b is the x-component of the force on q a maximum?
Ok so I know that when b is zero, there is no x component.
To solve the maz I did the following
Fx=kQq/(a+b)^2
soFx = (4πεQq/(a^2 +b^2))(b/dFx/db = ((4πεQq)/(a^2 +b^2)^1.5) -8πεQqb^2(1.5(a^2 +b^2)^0.5/(a^2 +b^2)^3
a^2 +b^2))= 4πεQqb/(a^2 +b^2)^1.5
I took the deriviative of Fx with respect to b,
dFx/db = ((4πεQq)/(a^2 +b^2)^1.5) -8πεQqb^2(1.5(a^2 +b^2)^0.5/(a^2 +b^2)^3 (I don't know if this is right)
to solve for b I got
b=a/sqrt(8a^2q)^3
I'm pretty sure this is not right since on the website I use to submit my homework, there is only one space below the a for the maxima.
Where I need to input my answers it says the following:
a) Minima when b=___ and also as b approaches infinity
b) Maxima when b= +-a/sqrt____
There's only space for one number on each blank. I assume a) is zero. but I don't know what to do with b.
A) For what values(s) of b is the x-component of the force on q a minimum?
B) For what values(s) of b is the x-component of the force on q a maximum?
Ok so I know that when b is zero, there is no x component.
To solve the maz I did the following
Fx=kQq/(a+b)^2
soFx = (4πεQq/(a^2 +b^2))(b/dFx/db = ((4πεQq)/(a^2 +b^2)^1.5) -8πεQqb^2(1.5(a^2 +b^2)^0.5/(a^2 +b^2)^3
a^2 +b^2))= 4πεQqb/(a^2 +b^2)^1.5
I took the deriviative of Fx with respect to b,
dFx/db = ((4πεQq)/(a^2 +b^2)^1.5) -8πεQqb^2(1.5(a^2 +b^2)^0.5/(a^2 +b^2)^3 (I don't know if this is right)
to solve for b I got
b=a/sqrt(8a^2q)^3
I'm pretty sure this is not right since on the website I use to submit my homework, there is only one space below the a for the maxima.
Where I need to input my answers it says the following:
a) Minima when b=___ and also as b approaches infinity
b) Maxima when b= +-a/sqrt____
There's only space for one number on each blank. I assume a) is zero. but I don't know what to do with b.