What Is the Force on a Square Loop in a Magnetic Field?

Click For Summary
SUMMARY

The force on a square loop in a magnetic field defined by B = kz (x-hat) is determined by the interaction of the magnetic field with the current I flowing counterclockwise through the loop. The misconception that the forces on the top and bottom segments of the loop cancel out is incorrect; instead, these forces add together due to the changing sign of z in the magnetic field and the nature of the cross-product. This results in a net force acting on the loop, which must be calculated to understand the overall effect of the magnetic field on the loop.

PREREQUISITES
  • Understanding of magnetic fields and their representation (e.g., B = kz (x-hat))
  • Knowledge of the right-hand rule for determining force direction in magnetic fields
  • Familiarity with the concept of current-carrying loops and their interaction with magnetic fields
  • Basic understanding of vector cross-products in physics
NEXT STEPS
  • Study the application of the Lorentz force law on current-carrying conductors
  • Learn about the Biot-Savart Law and its implications for magnetic fields around conductors
  • Explore the concept of magnetic torque on loops in magnetic fields
  • Investigate the effects of varying magnetic fields on induced currents (Faraday's Law)
USEFUL FOR

Physics students, electrical engineers, and anyone interested in electromagnetism and the behavior of current-carrying loops in magnetic fields.

wakko101
Messages
61
Reaction score
0
The problem:

Suppose that the magnetic field in some region has the form B = kz (x-hat). Find the force on a square loop (side a), lying in the yz plane and centered at the origin, if it carries a current I, flowing counterclockwise, when you look down the x axis.

When I try to visualize the direction of the four magnetic fields (one for each side) it seems to me that they would cancel out (one going to the right, one going to the left, one going up and one going down). I have information to the contrary so I'm wondering what it is I'm seeing that is wrong.

Cheers,
W. =)
 
Physics news on Phys.org
For the top & bottom portions of the loop (ie at fixed z), the sign of z changes, but so does the sign from the cross-product, thus the top & bottom parts do not cancel out, but rather add together.
 

Similar threads

Induced current and force on circular loop in varying magnetic field
  • · Replies 4 ·
Replies
4
Views
1K
B-field inside a linear magnetic sphere (in a uniform external B-field)
  • · Replies 8 ·
Replies
8
Views
4K
Lorentz transformations for electric and magnetic fields
  • · Replies 7 ·
Replies
7
Views
4K
How Long Does It Take for a Falling Square Loop to Clear a Magnetic Field?
  • · Replies 16 ·
Replies
16
Views
3K
What is the net force on the current loop?
  • · Replies 8 ·
Replies
8
Views
2K
Off-axis magnetic field between two current-carrying rectangular loops
  • · Replies 3 ·
Replies
3
Views
4K
Finding the magnetic field of a loop at far distances
  • · Replies 1 ·
Replies
1
Views
2K
How Does Current Direction Affect Magnetic Force on a Loop in a Uniform Field?
  • · Replies 2 ·
Replies
2
Views
5K
How to obtain correct negative sign in calculation of motional emf?
  • · Replies 2 ·
Replies
2
Views
1K
Understanding Torque in a Magnetic Field with Loop
  • · Replies 37 ·
2
Replies
37
Views
5K