Listrik Magnet 13.5 Hubungan Medan Listrik Induksi dan Medan Magnet Induksi

Summary

This lecture dives into the relationship between induced electric fields and magnetic fields, exploring Faraday's Law and its applications. Key topics include how changing magnetic flux induces an electromotive force (EMF), the use of Stokes' Theorem to relate electric and magnetic fields, and the differences between electrostatics and electrodynamics. The session includes practical examples, such as calculating induced electric fields in a circular loop with a time-varying magnetic field. The lecture ends with a homework assignment on self-inductance and mutual inductance, reinforcing the students' understanding of electromagnetic induction.

Takeaways

• 😀 Faraday's Law explains how a changing magnetic flux generates an induced electromotive force (EMF).
• 😀 The induced EMF results in an induced electric field, which is related to the rate of change of the magnetic field.
• 😀 The differential form of Faraday's Law is given by: ∇ × E = - ∂B/∂t, showing the relationship between the curl of the electric field and the time change in the magnetic field.
• 😀 The relationship between induced electric fields and changing magnetic fields in electrodynamics differs from electrostatics, where electric fields arise from charges.
• 😀 In electrodynamics, the divergence of the induced electric field is zero, i.e., ∇ · E = 0, because there are no charges causing the field.
• 😀 The example of a circular loop in a changing magnetic field demonstrates how to calculate the induced electric field using Faraday’s Law and the magnetic flux.
• 😀 The induced electric field (E) in the circular loop is proportional to the radius and the rate of change of the magnetic flux, with the relationship: E = - r² (∂B/∂t) / R.
• 😀 The direction of the induced electric field follows the right-hand rule, opposing the change in the magnetic field.
• 😀 Inductance, both self-inductance and mutual inductance, is briefly introduced, particularly for solenoids.
• 😀 Students are tasked with researching and calculating the self-inductance of a solenoid and the mutual inductance of concentric solenoids, with a deadline for submission.

Q & A

What is the relationship between induced electric fields and magnetic fields in this lecture?

The induced electric field is related to the changing magnetic flux through Faraday's law of induction. A time-varying magnetic field creates an electric field that circulates around it, which is described by the equation ∇ × E = -∂B/∂t.

What is Faraday's law of induction as discussed in the script?

Faraday's law of induction states that a changing magnetic flux through a loop induces an electromotive force (EMF) or induced electric field. This is mathematically expressed as ∮ E • dl = -dΦB/dt, where ΦB is the magnetic flux.

How is the concept of electric potential related to induced electromotive force (EMF)?

Induced EMF is similar to electric potential difference. In the context of an electric field induced by a changing magnetic field, it can be expressed as a potential difference arising from the change in the magnetic flux.

What is the significance of Stokes' theorem in this context?

Stokes' theorem is used to relate the line integral of the electric field around a closed loop to the surface integral of the curl of the electric field. It helps transition from the line integral form of Faraday's law to its differential form.

How does the script explain the relationship between the electric and magnetic fields in electromagnetism?

The script explains that in electromagnetism, the electric field and magnetic field are interconnected. A time-varying magnetic field induces an electric field, and this relationship is described through Maxwell's equations.

What happens when the electric field is induced by changing magnetic flux?

When the magnetic flux changes, an induced electric field is created. The direction of the induced electric field depends on the change in the magnetic field and can be determined using the right-hand rule or by analyzing the flux's variation.

What role does the divergence of electric and magnetic fields play in this lecture?

The divergence of the electric field is zero in the case of induced electric fields because they are not generated by charges. Similarly, the divergence of the magnetic field is also zero, which is consistent with Maxwell’s equations that describe the behavior of fields.

What is the physical interpretation of the rotation of the electric field in relation to magnetic fields?

The rotation of the electric field corresponds to the presence of a changing magnetic field. According to Faraday's law, the curl (rotation) of the electric field is related to the time derivative of the magnetic field, indicating that the electric field 'rotates' around the changing magnetic flux.

What does the script explain about the induced electric field in the context of an example with a circular coil?

In the example with a circular coil, a time-varying magnetic field induces an electric field around the coil. The induced electric field's direction depends on the changing magnetic flux, and it can be calculated using the relation between the electromotive force and the changing flux.

What is the difference between electrostatics and electrodynamics in the context of this script?

In electrostatics, the electric field is static, and the potential difference between two points in a closed loop is zero. In electrodynamics, the electric field is dynamic, and a changing magnetic field induces an electric field, leading to a non-zero electromotive force.