Distance from +4μC to Zero Potential: 24mm

AI Thread Summary
The discussion revolves around determining the distance from a +4 μC charge to a point where the electric potential is zero, given two charges, +4 μC and -16 μC, separated by 120 mm. The correct answer is identified as 24 mm, calculated using a ratio based on the charges' magnitudes. A participant expresses confusion about why only the magnitudes are used in calculations, leading to clarification that the correct approach involves setting the sum of potentials from both charges to zero. The participant acknowledges a mistake in their earlier calculations and decides to take a break to refocus on their studies. Understanding the principles of electric potential and charge interaction is crucial for solving such problems accurately.
mrcotton
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Homework Statement


photobucket4_zps0655b6ef.jpg

The diagram shows two charges, +4 μC and –16 μC, 120 mm apart. What is the distance from
the +4 μC charge to the point between the two charges where the resultant electric potential is
zero?
A 24mm
B 40mm
C 80mm
D 96mm

Homework Equations



potential equation

The Attempt at a Solution



photobucket3_zps880c633e.jpg

Homework Statement



The correct answer is a 24mm
I get that we could simply use a 1:4 ratio and therefore r must be a fifth of the way from the 4 micro coulomb charge
However when I try and equate the formula and solve algebraicaly I seem to get the wrong answer if I put in the sign of the charges.

So my question is why do we just use the magnitude of the charges?
 
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mrcotton said:
So my question is why do we just use the magnitude of the charges?
You seem to have written U1 = U2 when you should have used U1 + U2 = 0.
 


Thank you, I am a fool
I must take a break and do some maths in between my physics
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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