Hi. This originally a physics problem, but it's the mathematical
part that's giving me a headache.
The problem:
Vector E(net) = 2Ecos(theta)
E= Kq/[(x^2) + 0.25(s^2)] where K,q and s are constants
Theta= Tan^(-1)(0.5s/x)
Calculate Vector E(net)
My work:
1) cos (tan^(-1)x)=1/(1+x^2)^(1/2)
Cos(tan^(-1)(0.5s/x))= 1/[1+(0.25s^(2)/x^(2))]^(1/2)
= 1/[(x^(2)+0.25s^(2))/x^(2)]^(1/2)
= 1/[x*(x^(2)+0.25s^(2))^(1/2)]
2)E(net)= [2Kq/{(x^(2)+0.25s^(2)}]*[1/{x*(x^(2)+0.25s^(2))^(1/2)}]
= 2Kq/[x*(x^(2)+0.25s^(2))^(3/2)]
But my textbook says the answer is E(net)= 2Kqx/(x^(2)+0.25s^(2))^(3/2)
What am I doing wrong?
part that's giving me a headache.
The problem:
Vector E(net) = 2Ecos(theta)
E= Kq/[(x^2) + 0.25(s^2)] where K,q and s are constants
Theta= Tan^(-1)(0.5s/x)
Calculate Vector E(net)
My work:
1) cos (tan^(-1)x)=1/(1+x^2)^(1/2)
Cos(tan^(-1)(0.5s/x))= 1/[1+(0.25s^(2)/x^(2))]^(1/2)
= 1/[(x^(2)+0.25s^(2))/x^(2)]^(1/2)
= 1/[x*(x^(2)+0.25s^(2))^(1/2)]
2)E(net)= [2Kq/{(x^(2)+0.25s^(2)}]*[1/{x*(x^(2)+0.25s^(2))^(1/2)}]
= 2Kq/[x*(x^(2)+0.25s^(2))^(3/2)]
But my textbook says the answer is E(net)= 2Kqx/(x^(2)+0.25s^(2))^(3/2)
What am I doing wrong?
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