A currentcarrying wire is bent into a semicircular loop of radius r that lies in the xy plane. In a uniform magnetic field, a currentcarrying loop of wire, such as a loop in a motor, experiences both forces and torques on the loop. Bext the direction of the torque is to line up the dipole moment with the magnetic field. Physics 121 practice problem solutions 09 magnetic fields. Bottom side up, top side down rhr rotates around horizontal axis i. Torque on a bar magnet placed in a uniform magnetic field. A uniform magnetic field exerts no net force on a current loop but it does exert a net torque. Torque on a current carrying rectangular loop in a magnetic. Magnetic force on a current carrying wire top view f b. Niab sin where n is the number of turns in the coil, a is the area.
Consider a bar magnet ns of length 2l and pole strength m placed in a uniform magnetic field of induction b at an angle. Dec 20, 2017 this physics video tutorial explains how to calculate the torque on a current loop in a uniform magnetic field as well as the magnetic dipole moment. The loop carries a current \i\, has \n\ turns, each of area \ a \, and the perpendicular to the loop makes an angle \\theta\ with the field \b\. Torque on a current loop in a uniform magnetic field now suppose that the uniform magnetic. The loop is in a uniform magnetic field of magnitude 75. In a uniform magnetic field, a wire loop carrying current experiences no net force, but there is generally a net torque acting that tends to make the loop rotate. If there is another magnet magnetic field below it the south pole at a will be attracted or repelled straight up or straight do. A non uniform magnetic field can produce a net force, but it is more complex and we will not study it in this course here we will look at the torque on the. The potential energy is the least when and b are parallel and largest when and b are antiparallel. This equation can be shown to be valid for a loop of any shape. We take the magnetic field to be uniform over the rectangular loop, which has width w and height l.
Similarly on the side da,no magnetic force acts since current element makes an angle. Torque experienced by a current loop in a uniform magnetic field. Although this is generally true, there is a net torque on a current loop in an external field, and this torque tends to rotate the loop. Figure \\pageindex1\ shows a rectangular loop of wire that carries a current i and has sides of lengths a and b. Apr 10, 2018 a current carrying loop acts like a little magnet with north on one side of the loop and south on the other. Let theta be the angle between the normal to the plane of the loop and the direction of the magnetic field. We find that a rectangular loop carrying a steady current and placed in a.
Motion of a charged particle in a uniform magnetic field. Due to the magnetic field b, a force mb acts on the north pole along the direction of the field and a force mb. How to find the torque on a current loop in a magnetic field. Torque on a current loop in a magnetic field online science. The torque on a current loop boston university physics. This physics video tutorial explains how to calculate the torque on a current loop in a uniform magnetic field as well as the magnetic dipole moment.
In a uniform magnetic field, a current carrying loop of wire, such as a loop in a motor, experiences both forces and torques on the loop. There will be a net torque whose magnitude on this. First, we note that the forces on the top and bottom segments. Torque causes an object to spin around a fixed axis. The net torque acting on the coil has a magnitude given by. The torque on the loop and potential energy are calculated from identifying the magnetic moment, magnetic field, and angle oriented in the field. How to find the torque on a current loop in a magnetic field 1. Lets say the magnetic field is in the plane of the loop and is parallel to two sides.
Commonly used in electromagnets, devices used to convert electrical current to magnetic field. The magnetic moment of a current loop can be defined as the product of current flowing in the loop and the area of the rectangular loop. Here, a is a vector quantity with the magnitude equal to the area of the rectangular loop and the direction is given by the righthand thumb rule. When a current ipasses through a long straight wire, the magnetic field bis circular as is shown by the pattern of iron filings below and has the indicated direction. Torque on a current loop due to uniform magnetic field. Torque on current carrying coil in external magnetic field. If the magnet field is uniform then the net force on the current carrying loop due to magnetic field will be zero. Although the force on a closed loop of current in a uniform magnetic field is zero, the torque is not. A nonuniform magnetic field can produce a net force, but it is more complex and we will not study it in this course here we will look at the torque on the. Torque on current carrying loop definition, examples, diagrams. What is the direction of the net magnetic force on the current loop. Torque acting on a loop in a uniform magnetic field example a rectangular loop carrying a current i is placed in a uniform magnetic field b. Now we shall show that a steady current i passing through a rectangular loop placed in a uniform magnetic field.
The wire lies in the xy plane, and a uniform magnetic field is directed along the positive y axis as in figure 29. Various magnetic forces act on sections of a current carrying coil lying in a uniform external magnetic field, but the net force is zero. I dont understand why this isnt right, i got the first part right, it wanted me to find the magnetic dipole moment. If there are n turns in the loop, the torque acting on the loop is given by. Torque on current loop and magnetic moment derivation with. Apr, 2020 in terms of the magnetic dipole moment, the torque on a current loop due to a uniform magnetic field can be written simply as \\vec\tau \vec\mu \times \vecb.
Magnetic torques and amps law a magnetic field exerts a force on a straight wire carrying current. Potential energy of a current loop as the loop rotates because of the torque, the magnetic field does work on the loop we can talk about the potential energy of the loop and this potential energy is given by u b r r. A 3turn circular loop of radius 3 cm carries 5a current in. Force and torque on a current loop in uniform b field magnetic dipoles motion of a charged particle in a uniform b field applications.
This physics video tutorial explains how to calculate the torque on a current loop in a uniform magnetic field as well as the magnetic dipole. Magnetic field torque on a current loop physics forums. Force and torque on a current loop the net force on a current loop in a uniform magnetic field is zero. If the loop has a width a, a height b, and a current i, then the force on each of the left and right sides is f ibb.
Calculate the magnetic field magnetic field induced at the center of a loop loop or coil coil or at the interior of a solenoid. Torque on current loop iconsider rectangular current loop forces in left, right branches 0 forces in topbottom branches cancel no net force. This is ia, where iis the current and the magnitude of a is the area aenclosed by the loop. Torque on a current loop we showed that the net magnetic force on a closed current containing loop is zero when it is in a uniform magnetic field. Apr 01, 2009 a circular coil of 720 turns and area 0. This is the torque on a current carrying loop in a uniform magnetic field. This is the torque on a currentcarrying loop in a uniform magnetic field. Torque experienced by a current loop in uniform magnetic. A magnetic dipole is the limit of either a closed loop of electric current or a pair of poles as the dimensions of the source are reduced to zero while keeping the magnetic moment constant. The loop is placed in a uniform magnetic field of induction b. Mathematically, here, a is a vector quantity with the magnitude equal to the area of the rectangular loop and the direction is given by the righthand thumb rule. We have seen that the net magnetic force on a closed loop carrying a current is zero when the loop is placed in an external uniform magnetic field.
Force, torque on a current loop in a uniform magnetic field. Calculate the magnetic torque magnetic torque on a coil or solenoid of area a, turns n, and current i in a given bfield. Chapter 27 magnetic field and magnetic forces magnetism magnetic field magnetic field lines and magnetic flux motion of charged particles in a magnetic field applications of motion of charged particles magnetic force on a currentcarrying conductor force and torque on a current loop the directcurrent motor the hall effect. Forces on a current loop torque on a current loop in uniform. Potential energy since the magnetic dipole wants to line up with the magnetic field, it must have higher. What happens when we place a rectangular loop carrying a current i in the xy plane and switch on a uniform magnetic field. Torque on a current loop motors and meters physics. The force f 1 and f 2 are equal in magnitude, opposite in direction and have the same line of action.
If one defines a special area vector a, the magnitude of which is the area of the closed loop, and the direction of which is perpendicular to the plane of the loop as given by righthand rule, then the torque on the loop is. In this video we find an expression for the torque experienced by a current loop placed in a uniform magnetic field. Force and torque on a current loop physics libretexts. The loop carries a current i, has n turns, each of area a, and the perpendicular to the loop makes an angle. Stack of current loops solenoid when the loop are spaced together tightly enough, the b field inside is strong and rather uniform, and b field outside is essentially negligible. When a body is in equilibrium no net force on it and is rotating about an axis then the net torque on the body is independent of the choice of origin. What current carrying loop experiences are in a magnetic. Obtain an expression for the torque on a current carrying.
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