24. Electric Force & Field; Gauss' Law
Electric Charge
3PRACTICE PROBLEM
A rod of radius B is charged to a linear charge density λ. The volume charge density inside the rod (b ≤ B) is described by ρ (b) = bρ0 / B, where ρ0 is some unknown constant and ρ(b) has units C/m3. The charge on a volume element dV is dq = ρ dV. To get the total charge (Q = λY), we integrate dq = ρ dV over the entire length (Y) of the rod from zero to the radial length B. Determine the value of ρ0 in terms of λ and B. Hint: Find the volume of an element dV of length Y, radius b, and thickness db.
A rod of radius B is charged to a linear charge density λ. The volume charge density inside the rod (b ≤ B) is described by ρ (b) = bρ0 / B, where ρ0 is some unknown constant and ρ(b) has units C/m3. The charge on a volume element dV is dq = ρ dV. To get the total charge (Q = λY), we integrate dq = ρ dV over the entire length (Y) of the rod from zero to the radial length B. Determine the value of ρ0 in terms of λ and B. Hint: Find the volume of an element dV of length Y, radius b, and thickness db.
ANSWERS OPTIONS
A
ρ0 = 3λ / (πB3)
B
ρ0 = 3λ / (2πB2)
C
ρ0 = λ / (6πB2)
D
ρ0 = λ / (2πB3)