Physics help, kinda a tricky question.?
A 2.5 x 10 ^ -7 C charge initially at rest is 7.0 m from an 8.0 x 10 ^ -6 charge. What is the minimum work required to move the charge 2.5 x 10 ^ - 7 C 2.0m closer?
Question 2.
A proton moves with a constant speed of 3.6 x 10 ^ 5 m/s at right angles through a uniform 5.0 x 10 ^ -5 T magnetic field. What is the radius of curvature of the proton's motion?
Thanks in advance. I need help on these two questions.
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Verified answer
1)
Work done is:
R₂
W = ∫ F dR
R₁
where
R₁ = initial distance = 7 m
R₂ = final distance = (7 m) - (2 m) = 5 m
F = force
F = k × Q₁ × Q₂ / R²
where
k = constant of Coulomb = 9E9 Nm²/C²
Q₁ = one charge = 2.5E-7 C
Q₂ = other charge = 8E-6 C
R = distance
So:
5
W = ∫ [ (9E9) (2.5E-7) (8E-6) / R² ] dR
7
5
W = 0.018 ∫ [ 1 / R² ] dR
7
5
W = 0.018 [ -1 / R ]
7
W = 0.018 [ (-1/5) - (-1/7) ]
W = -0.001028 J
BUT... be careful here...
This is the work done by the electrostatic force!
The work done by the external force is:
W = 0.001028 J < - - - - - - - - - - - - - - - - - - - - - - - - - answer
2)
Fm = Fc
q × v × B = m × v² / R
R = (m × v) / (q × B)
where
R = radius of the curve = ?
m = mass of the proton = 1.67E-27 kg
v = speed of the proton = 3.6E5 m/s
q = charge of the proton = 1.6E-19 C
B = magnetic field = 5E-5 T
so
R = [ (1.67E-27) × (3.6E5) ] / [ (1.6E-19) × (5E-5) ]
R = 75.15 m