why the electric and magnetic fields are perpendicular to each other?
why we need ampere circuital law when we already have bio sevarts law?
why we use sin(theta) in the bio sevarts law why not the other ratios?
To understand why the electric and magnetic fields are generally perpendicular to each other, we need to consider Maxwell's equations. These equations describe the behavior of electromagnetic fields. Two of these equations, known as Faraday's law of electromagnetic induction and Ampere's law, provide insights into the relationship between electric and magnetic fields.
According to Faraday's law, a time-varying magnetic field induces an electric field. This means that the electric field is perpendicular to the changing magnetic field. On the other hand, Ampere's law states that a time-varying electric field induces a magnetic field. Therefore, the magnetic field resulting from the electric field is also perpendicular to it.
As a consequence of these two laws, the electric and magnetic fields are generally perpendicular to each other. This relationship is known as the electromagnetic field's fundamental property and has been observed through experimental observations.
Moving on to the second question, the Ampere's Circuital Law and the Bio-Savart Law are two different ways of expressing the same fundamental principle. Ampere's Circuital Law allows us to calculate the magnetic field around a closed loop by integrating the current passing through the loop. On the other hand, the Bio-Savart Law gives a formula for determining the magnetic field at a point in space due to a small current element.
While both laws describe the same physical phenomenon, they are used in different contexts. Ampere's Circuital Law is extremely useful for analyzing systems with symmetric currents or for calculating the total magnetic field around a given loop. In contrast, the Bio-Savart Law is often utilized to calculate the magnetic field at a specific point due to complex current distributions.
The choice of using sin(theta) in the Bio-Savart Law instead of other ratios depends on the geometry of the current distribution and the point where the magnetic field is being calculated. The sine function relates the angle (theta) between the current element and the line connecting the element to the point of interest. In some cases, other ratios like cosine or tangent may be used if they are more appropriate for describing the specific geometry of the problem. The appropriate choice of ratios depends on the specific circumstances and mathematical relationships involved in the problem at hand.