Find the force on each segment of the wire shown in Fig. 30-17 if B =0.15 T. Assume the current

Find the force on each segment of the wire shown in Fig....

Key Concepts

Lorentz Force Law

This law states that a current-carrying conductor placed within a magnetic field experiences a force given by F = I (L x B), where I is the current, L is the vector length of the conductor, and B is the magnetic field. This concept is the foundation for determining how magnetic fields interact with moving charges, leading to measurable forces on the conductor.

Vector Cross Product and Right-Hand Rule

The vector cross product is a mathematical operation used to determine both the magnitude and direction of the force when a current element interacts with a magnetic field. The right-hand rule provides a practical method for finding the direction of the force, which is perpendicular to both the current direction and the magnetic field.

Magnetic Interaction with Current-Carrying Conductors

This concept encompasses the overall understanding of how conductors carrying an electric current interact with external magnetic fields. It involves analyzing the impact of the orientation of the conductor relative to the magnetic field on the magnitude and direction of the exerted force, which is critical in various applications within electromagnetism.

Transcript

00:01 Hi, in this question, we want to find the force on the y in the segment.

00:08 And we have the magnetic field is in this direction and is equal to 0 .15 tesla.

00:18 And the current is flowing in the same direction as a magnetized field.

00:21 In this, for this first segment ab, so for segment ab, the current since the current in the same direction, it's parallel to the magnetic field.

00:31 There is no force because we needed the current to be perpendicular.

00:34 For that to be a force so for a b force is zero new turns now for c for bc we have the length of 16 centimeters l 16 centimeters which is equal to 0 .1 6 meters and when using f is equal to b i l cyan theta data data up 19 degrees because this perpendicular to the magnetic field destruction and so we have a f equal to 0 .1 .5 times the current we're giving that as 5 ampers.

01:16 So the current is equal to 5 ampers times 5 times length 0 .16.

01:25 9.

01:27 The force will be equal to and this equal to 0 .1 2 newtons.

01:35 So you're seeing the right hand out we can find the direction.

01:37 The thumb will be in the direction of the current the fingers being in the direction magnetic field so the the palm will face into the page and the direction is into the page now for section cd or section cd just to market this line now we have the length of the wire as 20 centimeters but the angle here is different and and so the angle here is 35 degrees from the vertical because the current should be perpendicular to the magnetic field.

02:27 So we need to resolve into the vertical.

02:31 So draw a triangle like this...

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