When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude I max of the current without disconnecting the wire to shunt the current through a meter. The Rogowski coil, shown in Figure P30.8, simply clips around the wire. It consists of a toroidal conductor wrapped around a circular return cord. Let n represent the number of turns in the toroid per unit distance along it. Let A represent the cross-sectional area of the toroid. Let I ( t ) = I max sin ωt represent the current to be measured. (a) Show that the amplitude of the emf induced in the Rogowski coil is E max = μ 0 n A ω I max . (b) Explain why the wire carrying the unknown current need not be at the center of the Rogowski coil and why the coil will not respond to nearby currents that it does not enclose. Figure P30.8
When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude I max of the current without disconnecting the wire to shunt the current through a meter. The Rogowski coil, shown in Figure P30.8, simply clips around the wire. It consists of a toroidal conductor wrapped around a circular return cord. Let n represent the number of turns in the toroid per unit distance along it. Let A represent the cross-sectional area of the toroid. Let I ( t ) = I max sin ωt represent the current to be measured. (a) Show that the amplitude of the emf induced in the Rogowski coil is E max = μ 0 n A ω I max . (b) Explain why the wire carrying the unknown current need not be at the center of the Rogowski coil and why the coil will not respond to nearby currents that it does not enclose. Figure P30.8
Solution Summary: The author explains the formula to calculate the magnetic field produced by the central wire.
When a wire carries an AC current with a known frequency, you can use a Rogowski coil to determine the amplitude Imax of the current without disconnecting the wire to shunt the current through a meter. The Rogowski coil, shown in Figure P30.8, simply clips around the wire. It consists of a toroidal conductor wrapped around a circular return cord. Let n represent the number of turns in the toroid per unit distance along it. Let A represent the cross-sectional area of the toroid. Let I(t) = Imax sin ωt represent the current to be measured. (a) Show that the amplitude of the emf induced in the Rogowski coil is
E
max
=
μ
0
n
A
ω
I
max
. (b) Explain why the wire carrying the unknown current need not be at the center of the Rogowski coil and why the coil will not respond to nearby currents that it does not enclose.
Example
Two charges, one with +10 μC of charge, and
another with - 7.0 μC of charge are placed in
line with each other and held at a fixed distance
of 0.45 m. Where can you put a 3rd charge of +5
μC, so that the net force on the 3rd charge is
zero?
*
Coulomb's Law Example
Three charges are positioned as seen below. Charge
1 is +2.0 μC and charge 2 is +8.0μC, and charge 3 is -
6.0MC.
What is the magnitude and the direction of the force
on charge 2 due to charges 1 and 3?
93
kq92
F
==
2
r13 = 0.090m
91
r12 = 0.12m
92
Coulomb's Constant: k = 8.99x10+9 Nm²/C²
✓
Make sure to draw a Free Body Diagram as well
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