A)<span>
dQ = ρ(r) * A * dr = ρ0(1 - r/R) (4πr²)dr = 4π * ρ0(r² -
r³/R) dr
which when integrated from 0 to r is
total charge = 4π * ρ0 (r³/3 + r^4/(4R))
and when r = R our total charge is
total charge = 4π*ρ0(R³/3 + R³/4) = 4π*ρ0*R³/12 = π*ρ0*R³ / 3
and after substituting ρ0 = 3Q / πR³ we have
total charge = Q ◄
B) E = kQ/d²
since the distribution is symmetric spherically
C) dE = k*dq/r² = k*4π*ρ0(r² - r³/R)dr / r² = k*4π*ρ0(1 -
r/R)dr
so
E(r) = k*4π*ρ0*(r - r²/(2R)) from zero to r is
and after substituting for ρ0 is
E(r) = k*4π*3Q(r - r²/(2R)) / πR³ = 12kQ(r/R³ - r²/(2R^4))
which could be expressed other ways.
D) dE/dr = 0 = 12kQ(1/R³ - r/R^4) means that
r = R for a min/max (and we know it's a max since r = 0 is a
min).
<span>E) E = 12kQ(R/R³ - R²/(2R^4)) = 12kQ / 2R² = 6kQ / R² </span></span>
Answer: 16N
Explanation:
Given that:
mass of box M= 2 kg
Initial speed V1 = 4 m/s
Final speed V2 = 8 m/s
Time taken T= 0.5 s
Average strength of this force F = ?
Now, recall that Force is the rate of change of momentum per unit time
i.e Force = momentum / time
Hence, F = M x (V2 - V1)/T
F = 2kg x (8 m/s - 4 m/s) / 0.5s
F = 2kg x (4 m/s / 0.5s)
F = 2kg x 8 m/s/s)
F = 16N
Thus, the average strength of this
force is 16 newton.
Answer:
, charges are both positive or both negative
Explanation:
The electrostatic force between the two spheres is given by
where
k is the Coulomb's constant
q1 and q2 are the charges on the two spheres
r is the distance between the centres of the two spheres
In this problem, we have
is the force
is the distance between the spheres
because the two spheres have identical charge
Solving the formula for q, we find
And the two charges have the same sign (so, both positive or both negative), since the sign of the force is positive (+0.30 N), so it is a repulsive force.
Explanation:
Work is the product of force and distance.
W = F×d
W = (22 N) × (16 m)
W = 352 J
