A rectangular loop of wire, carrying current I1= 2.0 mA, is next to a very long wire carrying a

A rectangular loop of wire, carrying current I1= 2.0 mA, is...

Key Concepts

Non-uniform Magnetic Fields and Net Force on Loops

When a current loop is placed in a non-uniform magnetic field, different segments of the loop experience different magnetic field strengths, leading to forces that may not cancel out completely. This results in a net force or torque acting on the loop. Understanding how the magnetic field strength varies with distance and how it affects different sections of the loop is key for accurately predicting net forces in such configurations.

Right-Hand Rule for Determining Directions

The right-hand rule is a fundamental tool used to determine the direction of both the magnetic field around a wire and the magnetic force on a current-carrying conductor. By aligning your thumb with the current, you can see how your fingers curl to indicate the magnetic field direction, and by orienting your hand according to the vectors in the cross product F = I (L × B), you can predict the force direction. This rule is indispensable for analyzing the magnetic interactions in circuits.

Lorentz Force on Current-Carrying Wires

A current-carrying wire in a magnetic field experiences a force described by the equation F = I (L × B), where I is the current, L is the length vector of the section of the wire, and B is the magnetic field. The cross product indicates that the direction of the force is perpendicular to both the current direction and the magnetic field, making the right-hand rule essential for determining force direction on each segment of the wire.

Magnetic Field from a Long Straight Conductor

A long, straight current-carrying wire produces a magnetic field whose magnitude is given by B = (??I)/(2?r), where I is the current and r is the distance from the wire. The field circulates around the wire according to the right-hand rule, meaning if you point your thumb along the current, your fingers curl in the direction of the magnetic field lines. This concept is crucial for understanding how the magnetic field varies across space and how it interacts with nearby conductors.

Transcript

00:01 Hi, in the given problem, first of all there is a long straight current carrying conductor which is carrying current towards right.

00:14 The current is i2 whose magnitude is given as 8 .0 ampere.

00:27 Then above this long straight current carrying conductor there is a rectangle rectangular loop carrying current i1 in clockwise direction like this and this current is i1 whose magnitude is given as 2 .0 millie ampere the gap between the long conductor and the lower arm of this rectangular loop it is given as a is equal to 2 .0 centimeter width of this loop that is given as 5 .0 centimeter and if we consider the length to be l its value is given as 9 .0 centimeter.

01:32 Now in the first part of the problem we have to find the directions of all the forces experienced by all these four arms of the rectangular current carrying coil for which first of all direction of magnetic field due to this current carrying conductor i2 above it that direction will be out of the plane of paper perpendicularly everywhere which is shown with the help of dots like this so using right hand thumb rule, the direction of magnetic field due to current i2 above the conductor is outward perpendicular to the plane of paper.

03:03 So, now using fleming's left -hand rule, which is a rule used to find the direction of force experienced by a current carrying conductor when it is kept in an external magnetic field.

03:30 So, using fleming's left -hand rule, directions of forces, is on the arms of loop, rectangular loop, are as shown in the figure.

04:06 First of all, if we consider this width, the left arm, left width of the coil, it will experience a force f1 towards right.

04:19 Similarly, its opposite arm, it will experience the same force.

04:25 F2 but towards left.

04:28 The lower most arm, horizontal arm, it will experience a force f3 upward and the uppermost arm it will experience a force f4 downward...

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