The quantity of charge q (in coulombs) that has passed through a surface of area 2.10 cm2 varies with time according to the equation q
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Original Question : The quantity of charge q (in coulombs) that has passed through a surface of area 2.10 cm2 varies with time according to the equation q = 4t3 + 5t + 6, where t is in seconds.
(a) What is the instantaneous current through the surface at t = 1.04 s?
in A
(b) What is the value of the current density?
kA/m2
q = 4t³ + 5t +6
dt/dt = 12t² + 5
t = 1. 04 seconds
Q = dq/dt = 12t² + 5 = 12(1.04)² + 5 =
Q = 17.97 C
I = Q/t
= 17.97/1.04 = 17.28 A
Current density = J = I/S
S = 2.1 cm² = 2.1 x 10⁻⁴ m²
J = 17.28 x 10⁴ / 2.1 = 8.22 x 10⁴ A m⁻²
(a) What is the instantaneous current through the surface at t = 1.04 s?
in A
(b) What is the value of the current density?
kA/m2
q = 4t³ + 5t +6
dt/dt = 12t² + 5
t = 1. 04 seconds
Q = dq/dt = 12t² + 5 = 12(1.04)² + 5 =
Q = 17.97 C
I = Q/t
= 17.97/1.04 = 17.28 A
Current density = J = I/S
S = 2.1 cm² = 2.1 x 10⁻⁴ m²
J = 17.28 x 10⁴ / 2.1 = 8.22 x 10⁴ A m⁻²
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