Capacitance ~
Magnetic Field in the Plane of the Loop
KOCW – 전자기학(전자정보공학과 오창현 교수)
11강 강의자료
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Capacitance
• When separated by an insulating (dielectric) medium, any two conducting bodies, regardless of their shapes and sizes, form a capacitor.
When a conductor has excess charge, it distributes the charge on its surface in such a manner as to maintain a zero electric field everywhere within the conductor, thereby ensuring that the electric potential is the same at every point in the conductor.
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Capacitance
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Electrostatic Potential Energy
• The energy ends up getting stored in the dielectric medium in the form of electrostatic potential energy. The amount of stored energy 𝑊𝑒 is related to Q, C, and V.
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Electrostatic Potential Energy
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• The electrostatic energy density 𝓌𝑒 is defined as the electrostatic potential energy 𝑊𝑒 per unit volume
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Electrostatic Potential Energy
• The mechanical work is provided by expending electrostatic energy.
Hence, 𝑑𝑊 equals the loss of energy stored in the dielectric insulating material of the capacitor, or
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Image Method
• Any given charge configuration above an infinite, perfectly conducting plane is electrically equivalent to the combination of given charge configuration and its image configuration, with the conducting plane removed.
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Image Method
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Chapter 5.
Magnetostatics
Overview
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Overview
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Magnetic Forces and Torques
• The electric force 𝐅𝑒 per unit charge
• Magnetic flux density B
• Particle charge q moving with velocity u
• If a charged particle resides in the presence of both an electric field E and a magnetic field B, then the total Electromagnetic force acting on it is
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[Newton / (Coulomb*meter/sec)]=[Tesla]
Magnetic Forces and Torques
• The force expressed by Eq.(5.5) also is known as the Lorentz force.
Electric and magnetic forces exhibit a number of important differences
1. Whereas the electric force is always in the direction of the electric field, the magnetic force is always perpendicular to the magnetic field.
2. Whereas the electric force acts on a charged particle whether or not it is moving, the magnetic force acts on it only when it is in motion.
3. Whereas the electric force expends energy in displacing a charged particle, the magnetic force does no work when a particle is displaced.
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Magnetic Forces and Torques
• Hence, the work performed when a particle is displaced by a differential distance 𝑑𝐈 = 𝐮 is
Since no work is done, a magnetic field cannot charge the kinetic energy of a charged particle; the magnetic field can charge the direction of motion of a charged particle, but not its speed.
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Magnetic Force on a Current-Carrying Conductor
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Magnetic Force on a Current-Carrying Conductor
QuB : C x (m/sec) x Tesla I l B : (C/sec) x m x Tesla
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This result, which is a consequence of the fact that the vector sum of the infinitesimal vectors dI over a closed path equals zero, states that the total magnetic force on any closed current loop in a uniform magnetic field is
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Magnetic Force on a Current-Carrying Conductor
Magnetic Torque on a Current-Carrying Loop
• The moment arm (called the torque)
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These directions are governed by the following right-hand rule: when the thumb of the right hand points along the direction of the torque, the four fingers indicate the direction that the torque tries to rotate the body.
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Magnetic Field in the Plane of the Loop
• The loop lies in the x-y plane and is allowed to pivot about the axis shown.
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