Charge Distribution and Work

[sweetsaja]

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This is from Kaplan High-Yield Problem Solving Guide pg. 63 Charge Distribution and Work

W=deltaU=qdeltaV
V=(kq/r) + (kq/r)
W=4*10^-6{[(9*10^9)(1*10^-6)]/(2*10^-3)}+{[(9*10^9)(-2*10^-6)]/(1*10^-3)}=18-72=-54J


I feel like im missing something stupid? I get -54*10^-6J Where does the 10^-6 disappear?

 

[G1SG2]

This is from Kaplan High-Yield Problem Solving Guide pg. 63 Charge Distribution and Work

W=deltaU=qdeltaV
V=(kq/r) + (kq/r)
W=4*10^-6{[(9*10^9)(1*10^-6)]/(2*10^-3)}+{[(9*10^9)(-2*10^-6)]/(1*10^-3)}=18-72=-54J


I feel like im missing something stupid? I get -54*10^-6J Where does the 10^-6 disappear?

10^-6{[(9*10^9)(1*10^-6)]/(2*10^-3)}:

Once you divide by 2*10^-3, you add the 10^-3, so you get:

10^-6{[(9*10^9)(1*10^-6)] * 10^3 (remember, exponents from the denominator become positive when you divide). So just looking at the exponents, we now have 10^-6 * 10^9 * 10^-6 * 10^3. When you multiply powers, you add the exponents. (-6)+ (9) + (-6) + (3)=0! The powers disappear.