Answer:
a) 1.082 × 10⁻¹⁹C ( e = 1.6 × 10⁻¹⁹C)
b) 3.466 × 10¹¹ N/C
Explanation:
a)
p(r) = -A exp ( - 2r/a₀)
Q = ₀∫^∞ ₀∫^π ₀∫^2xπ p(r)dV = -A ₀∫^∞ ₀∫^π ₀∫^2π exp ( - 2r/a₀)r² sinθdrdθd∅
Q = -4πA ₀∫^∞ exp ( - 2r/a₀)r²dr = -e
now using integration by parts;
A = e / πa₀³
p(r) = - (e / πa₀³) exp (-2r/a₀)
Now Net charge inside a sphere of radius a₀ i.e Qnet is;
= e - (e / πa₀³) ₀∫^a₀ ₀∫^π ₀∫^2π r² exp (-2r/a₀)dr
= e - e + 5e exp (-2) = 1.082 × 10⁻¹⁹C ( e = 1.6 × 10⁻¹⁹C)
b)
Using Gauss's law,
E × 4πa₀ ² = Qnet / ∈₀
E = 4πa₀ ² × Qnet × 1/a₀²
E = 3.466 × 10¹¹ N/C
The heat released by the water when it cools down by a temperature difference
is
where
m=432 g is the mass of the water
is the specific heat capacity of water
is the decrease of temperature of the water
Plugging the numbers into the equation, we find
and this is the amount of heat released by the water.
The force on the proton is 17.4 N.
<h3>What is the force on the proton?</h3>
Now we know that the proton is positively charged and that the force on the charge as it moved through the magnetic field could be given by the relation; F = qvB
Where;
F = force
q = charge
v = velocity
B = magnetic field
Having said this, we can see that;
q = 1.601019 As or C
v = 2.4105 m/s
T = 4.5 T
F = 1.601019 As * 2.4105 m/s * 4.5 T
F = 17.4 N
Learn more about magnetic force:brainly.com/question/12824331
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To change from mass to weight is Fw = 30 kg * 9.8 m/s^2 = 294 N. To change from weight to mass divide by gravity (9.8 m/s^2).
