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Chapter 15: Problem 2117

According to Maxwell, a changing electric field produces (A) emf (B) Electric current (C) magnetic field (D) radiation pressure

Short Answer

Expert verified
According to Maxwell's equations, specifically Ampère-Maxwell's Law, a changing electric field produces a magnetic field. So the correct answer is (C) magnetic field.

Step by step solution

01

Understanding Maxwell's Equations

To answer this question, we need to have a basic understanding of Maxwell's equations, which are a set of four equations describing the behavior of electric and magnetic fields. The equations are: 1. Gauss's Law for Electric Fields: \(\oint \vec{E} \cdot \mathrm{d} \vec{A} = \frac{Q}{\epsilon_0}\) 2. Gauss's Law for Magnetic Fields: \(\oint \vec{B} \cdot \mathrm{d} \vec{A} = 0\) 3. Faraday's Law of Electromagnetic Induction: \(\oint \vec{E} \cdot \mathrm{d} \vec{l} = -\frac{d\Phi_B}{dt}\) 4. Ampère-Maxwell's Law: \(\oint \vec{B} \cdot \mathrm{d} \vec{l} = \mu_0 \left( I + \epsilon_0 \frac{d\Phi_E}{dt} \right)\) From these equations, we can deduce the effect of a changing electric field.
02

Relating Changing Electric Field to Maxwell's Equations

In this case, we need to look at the Ampère-Maxwell's Law, as it contains the term \(\frac{d\Phi_E}{dt}\), which represents the rate of change of the electric field. Ampère-Maxwell's Law: \(\oint \vec{B} \cdot \mathrm{d} \vec{l} = \mu_0 \left( I + \epsilon_0 \frac{d\Phi_E}{dt} \right)\) This equation tells us that a changing electric field, represented by the term \(\frac{d\Phi_E}{dt}\), will generate a magnetic field (denoted by \(\vec{B}\)).
03

Identifying the Correct Option

Now that we know a changing electric field generates a magnetic field, we can look at the given options and identify the correct one: (A) emf: A changing magnetic field generates emf, not a changing electric field. (B) Electric current: Electric current is not directly produced by a changing electric field. (C) magnetic field: As we found in our analysis, a changing electric field generates a magnetic field. (D) radiation pressure: Radiation pressure is not directly related to a changing electric field. The correct answer is (C) magnetic field.

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