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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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Most popular questions from this chapter

The wavelength of \(\mathrm{x}\) rays is of the order of (A) \(10^{-3} \mathrm{~m}\) (B) \(10^{-5} \mathrm{~m}\) (C) \(10^{-10} \mathrm{~m}\) (D) \(10^{-12} \mathrm{~m}\)

The velocity of light in vacuum can be changed by changing (A) frequency (B) wavelength (C) amplitude (D) none of these

Unit of \(\mu_{0} \mathrm{c}\) is same as that of (A) current (B) resistance (C) electric charge (D) velocity

If the wavelength of light is \(4000^{\circ} \mathrm{A}\) then the number of waves in \(1 \mathrm{~mm}\) length will be (A) \(2.5\) (B) 2500 (C) 250 (D) 25000

The maximum value of \(\mathrm{E}^{-}\) in an electromagnetic waves in air is equal to \(6.0 \times 10^{-4} \mathrm{Vm}^{-1}\). The maximum value of \(\mathrm{B}^{-}\) is (A) \(1.8 \times 10^{5} \mathrm{~T}\) (B) \(2.0 \times 10^{4} \mathrm{~T}\) (C) \(2.0 \times 10^{-12} \mathrm{~T}\) (D) \(1.8 \times 10^{13} \mathrm{~T}\)
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