Magnetic Field PDF

Magnetic Field Two loops of wire carrying currents I1 and I2 Ampère’s law of force  Magnetic forces associated with two loops of wire carrying currents by virtue of motion of charges in the loops.  Two loops of wire carrying currents I1 and I2 and each...

Magnetic Field Two loops of wire carrying currents I1 and I2 Ampère’s law of force  Magnetic forces associated with two loops of wire carrying currents by virtue of motion of charges in the loops.  Two loops of wire carrying currents I1 and I2 and each of which is divided into m and n number of elements having infinitesimal lengths respectively.  The total force experienced by a loop is the vector sum of forces experienced by the infinitesimal current elements constituting the loop.  The force experienced by each of these current elements is the vector sum of the forces exerted on it by the infinitesimal current elements constituting the second loop.  consider an element dl1 in loop 1 and an element dl2 in loop 2, then the forces dF1 and dF2 experienced by the elements dl1 and dl2 respectively, are given by where a12 and a21 are unit vectors along the line joining the two current elements, R is the distance between them. 1. The magnitude of the force is proportional to the product of the two currents and to the product of the lengths of the two current elements. 2. The magnitude of the force is inversely proportional to the square of the distance between the current elements. 3. Force dF1 and dF2 which are not equal and opposite.  Let us consider at (1, 0, 0) and at (0, 1, 0).Then For the differential current elements, but isolated current elements does not exist without sources and sinks. Thus Newton’s third law must and does hold for complete current loops. Magnetic flux density dF1 and dF2 suggests that the each current element is acted on by a field which is due to the other current element. This field is the MF and is characterized by a quantity known as magnetic flux density vector. Magnetic flux density at the element dl2 due to the element dl1 is given by B1 acting on dl2 results in a force on it given by, Similarly, the magnetic flux density at the element dl1 due to the element dl2 is given by, B2 acting on dl1 results in a force on it given by, i.e. an infinitesimal current element of length dl and current I placed in a magnetic field of flux density B experiences a force dF given by Magnetic Field due to a current element-Biot Savart Law the magnetic flux density due to an infinitesimal current element of length dl and carrying current I to be, Force experienced by a current element in a MF. where R is the distance from the current element to the point at which the flux density is to be computed and aR is the unit vector along the line joining the current element and the point under consideration and directed away from the current element.  The Biot–Savart law states that the magnitude of B at a point P is proportional to the current I, the element length dl, and the sine of the angle α between the current element and the line joining it to the point P, and is inversely proportional to the square of the distance from the current elementto the point P.  Hence, the magnetic flux density is zero at points along the axis of the current element and increases in magnitude as the point P is moved away from the axis on a spherical surface centered at the current element, becoming a maximum for equal to 90°.  This is in contrast to the behavior of the electric field intensity due to a point charge, which remains the same in magnitude at points on a spherical surface centered at the point charge.  The direction of B at point P is normal to the plane containing the current element and the line joining the current element to P as given by the cross product operation , that is, right circular to the axis of the wire.  The direction lines of the magnetic flux density due to a current element are circles centered at points on the axis of the current element and lying in planes normal to the axis. But the direction lines of the electric field intensity due to a point charge, which are radial lines emanating from the point charge.