A toroid has a major radius R and a minor radius r and is tightly wound with N turns of wire on a hollow cardboard torus. Figure P31.6 shows half of this toroid, allowing us to see its cross section. If R >> r , the magnetic field in the region enclosed by the wire is essentially the same as the magnetic field of a solenoid that has been bent into a large circle of radius R . Modeling the field as the uniform field of a long solenoid, show that the inductance of such a toroid is approximately L = 1 2 μ 0 N 2 r 2 R Figure P31.6
A toroid has a major radius R and a minor radius r and is tightly wound with N turns of wire on a hollow cardboard torus. Figure P31.6 shows half of this toroid, allowing us to see its cross section. If R >> r , the magnetic field in the region enclosed by the wire is essentially the same as the magnetic field of a solenoid that has been bent into a large circle of radius R . Modeling the field as the uniform field of a long solenoid, show that the inductance of such a toroid is approximately L = 1 2 μ 0 N 2 r 2 R Figure P31.6
Solution Summary: The author explains the inductance of the toroid under the uniform field approximation as a case of solenoid.
A toroid has a major radius R and a minor radius r and is tightly wound with N turns of wire on a hollow cardboard torus. Figure P31.6 shows half of this toroid, allowing us to see its cross section. If R >> r, the magnetic field in the region enclosed by the wire is essentially the same as the magnetic field of a solenoid that has been bent into a large circle of radius R. Modeling the field as the uniform field of a long solenoid, show that the inductance of such a toroid is approximately
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
✓
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