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Magnetic Fields: Exploring Forces on Moving Charges and Current-Carrying Wires
What Are Magnetic Fields?
A magnetic field is a region where magnetic forces act on moving charges or magnetic materials.
Key Concepts in Magnetic Fields
Magnetic Force on a Moving Charge
A charge ![[q]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-e4373fc0a950fb903e00165c542f95c4_l3.png "Rendered by QuickLaTeX.com")
moving in a magnetic field ![[B]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-28b42a6e6a2c07f3ed58ce87b6856f18_l3.png "Rendered by QuickLaTeX.com")
experiences a force:
![\[ \mathbf{F} = qvB \sin\theta \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-757117e01a27a9f4b66cca8a1032790b_l3.png "Rendered by QuickLaTeX.com")
Where:
: Force (N).
: Charge (C).
: Velocity (m/s).
: Angle between 
and 
.
: Force (N).
: Charge (C).
: Velocity (m/s).
: Angle between 
and 
.Magnetic Force on a Current-Carrying Wire
A wire with current ![[I]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-e620fa48094760bf56e357e8b427a43e_l3.png "Rendered by QuickLaTeX.com")
in a magnetic field experiences a force:
![\[ F = BIL \sin\theta \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-356e0092f4ef997893cd292013ef0ea6_l3.png "Rendered by QuickLaTeX.com")
Where:
- : Length of the wire (m).
: Length of the wire (m).Applications of Magnetic Fields
Motors and Generators
Convert electrical energy to mechanical energy and vice versa.
Magnetic Resonance Imaging (MRI)
Uses strong magnetic fields to create detailed images of the human body.
Particle Accelerators
Guide charged particles in circular paths.
Example Problem
A 
wire carries a current of 
in a 
magnetic field at 
. Find the force on the wire.
- Formula:
- Substitute Values:
![\[ F = BIL \sin\theta \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-bea80a96f9f5edd46a32d07cdc0f1c2a_l3.png "Rendered by QuickLaTeX.com")
![\[ F = (0.2)(5)(1)\sin 90^\circ = 1 \, \text{N} \]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-f235b068b3991e0581a636082ad0671c_l3.png "Rendered by QuickLaTeX.com")
Common Mistakes
- Forgetting
. - Confusing
![[F = qvB \sin\theta]](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMTIiIGhlaWdodD0iMTgiIHZpZXdCb3g9IjAgMCAxMTIgMTgiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+ "Rendered by QuickLaTeX.com")
and ![[F = BIL \sin\theta]](data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIxMTUiIGhlaWdodD0iMTgiIHZpZXdCb3g9IjAgMCAxMTUgMTgiPjxyZWN0IHdpZHRoPSIxMDAlIiBoZWlnaHQ9IjEwMCUiIHN0eWxlPSJmaWxsOiNjZmQ0ZGI7ZmlsbC1vcGFjaXR5OiAwLjE7Ii8+PC9zdmc+ "Rendered by QuickLaTeX.com")
. - Ignoring the right-hand rule for direction.
.![[F = qvB \sin\theta]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-77edba82aa2442697a9e77caf046e745_l3.png "Rendered by QuickLaTeX.com")
and ![[F = BIL \sin\theta]](https://skinattuition.co.uk/core/ql-cache/quicklatex.com-accc318761609c97de5f3f2136668946_l3.png "Rendered by QuickLaTeX.com")
.Practice Questions
- Calculate the force on a
wire carrying 
in a 
field at 
. - Explain how motors use magnetic fields.
- Describe an application of magnetic force on charges.
wire carrying 
in a 
field at 
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