Problem #1
During the 4.0 min a 5.0 A current is set up in a wire, how many (a) coulombs and (b) electrons pass through any cross section across the wire’s width?Answer;
Time, Δt = 4.0 min = 240 s
Current, i = 5.0 A
(a) electrical charge is,
Δq = iΔt = (5.0 A)(240 s) = 1200 C
(b) electrons pass through any cross section across the wire’s width is
n = Δq/e = 1200 C/(1.6 x 10-19 C) = 7.5 x 1021 elektrons
Problem #2
An isolated conducting sphere has a 10 cm radius. One wire carries a current of 1.000 002 0 A into it. Another wire carries a current of 1.000 000 0 A out of it. How long would it take for the sphere to increase in potential by 1000 V?
Answer;
The charge on the sphere after t seconds is:
q = (1.000002 – 1.000000)t = 0.000002t
the voltage on the surface is:
V = kq/R = k(0.000002t)/R
Solve for t:
t = (RV)/(0.000002k) = (0.10 x 1000)/(0.000002 x 9 x 109) = 5.56 ms
Problem #3
A charged belt, 50 cm wide, travels at 30 m/s between a source of charge and a sphere.The belt carries charge into the sphere at a rate corresponding to 100 μA. Compute the surface charge density on the belt.
Answer:
Known:
Velocity, v = 30 m/s
Current, i = 100 mA = 100 x 10-3 A
The charge is ‘dq’:
dq = idt
the surface is dA:
dA = Ldx
charge density is:
σ = dq/dA
σ = idt/Ldx
σ = i/Lv
= (100 x 10-6 A)/[(0.5 m)(30 m/s)]
σ = 6.7 x 10-6 C/m2 = 6.7 μC/m2
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