The electric field in an electromagnetic wave is moving in a free space given as vec \(E =E_ 0 \;sin(⍵t - kz)\) \(i\) The corresponding magnetic field will be:
- \(\frac{E_0}{ c}\; sin(⍵t - kz) \hat j\)
- \(\frac{E_0}{c}\; sin(⍵t - kz) \hat j\)
- \(\frac{E_0}{c}\; cos(⍵t - kz) \hat i\)
- \(\frac{E_0}{c} \;sin(⍵t - kz) \hat i\)
The Correct Option is B
Solution and Explanation
The Correct Option is (B): \(\frac{E_0}{c}\; sin(⍵t - kz) \hat j\)
Top Questions on Magnetic Field
A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field \( B \) exists into the page. The bar starts to move from the vertex at time \( t = 0 \) with a constant velocity. If the induced EMF is \( E \propto t^n \), then the value of \( n \) is _____.
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Ferromagnetic substances are those which get strongly magnetized when placed in an external magnetic field. They have strong tendency to move from a region of weak magnetic field to strong magnetic field, that is, they get strongly attracted to a magnet. The individual atoms (or ions or molecules) in a ferromagnetic material possess a dipole moment as in a paramagnetic material. However, they interact with one another in such a way that these spontaneously align themselves in a common direction over a macroscopic volume called domain. Each domain has a net magnetization. Typical domain size is 1 mm and the domain contains about \(10^{11}\) atoms. In the first instant the magnetization varies randomly from domain to domain and there is no bulk magnetization. When we apply an external magnetic field \(B_0\) the domains orient themselves in the direction of \(B_0\) and simultaneously that domain oriented in the direction of \(B_0\) grows in size. We may wonder as to what happens when the external field is removed, in some ferromagnetic materials the magnetization persists. Such materials are called hard magnetic materials of hard magnets. Alnico, an alloy of iron, aluminium, nickel, cobalt and copper is one such material. There is a class of magnetic materials in which the magnetization disappears on removal of the external field. Soft iron is one such material. Such materials are called soft ferromagnetic materials. There are number of elements which are ferromagnetic. Iron, cobalt, Nickel, gadolinium etc. The ferromagnetic property depends on temperature. At high enough temperature a ferromagnet becomes a paramagnet. That domain structure disintegrates with temperature. This disappearance of magnetization with the temperature is gradual.- PSEB XII - 2025
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Concepts Used:
Magnetic Field
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
- Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
- Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
Properties of Magnetic Field Lines
- Magnetic field lines never cross each other
- The density of the field lines indicates the strength of the field
- Magnetic field lines always make closed-loops
- Magnetic field lines always emerge or start from the north pole and terminate at the south pole.