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184_notes:i_b_force [2018/07/19 13:19] – [Force on a little chunk] curdemma | 184_notes:i_b_force [2018/07/19 13:30] – [Force on the whole wire] curdemma | ||
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using the fact that $\frac{dq}{dt}$ is the definition of conventional current (the amount of charge passing a point per second). | using the fact that $\frac{dq}{dt}$ is the definition of conventional current (the amount of charge passing a point per second). | ||
- | {{ 184_notes: | + | [{{ 184_notes: |
This means that the small amount of force on the wire is given by: | This means that the small amount of force on the wire is given by: | ||
$$d\vec{F}= I d\vec{l} \times \vec{B}$$ | $$d\vec{F}= I d\vec{l} \times \vec{B}$$ | ||
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Here we want to pick the limits of the integral to be from the starting point of the wire ($l_i$) to the end of the wire ($l_f$) so we are adding up over the whole length of the wire. This form of the force will //always// work to find the magnetic force on the whole wire - we have not made very many assumptions so far in coming up with this equation. | Here we want to pick the limits of the integral to be from the starting point of the wire ($l_i$) to the end of the wire ($l_f$) so we are adding up over the whole length of the wire. This form of the force will //always// work to find the magnetic force on the whole wire - we have not made very many assumptions so far in coming up with this equation. | ||
- | However, if we do make a few assumptions we can simplify this equation significantly. We will start by // | + | However, if we do make a few assumptions we can simplify this equation significantly. We will start by // |
$$\vec{F}_{wire}= I \int_{l_i}^{l_f} d\vec{l} \times \vec{B}$$ | $$\vec{F}_{wire}= I \int_{l_i}^{l_f} d\vec{l} \times \vec{B}$$ | ||
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$$|\vec{F}_{wire}|=IBLsin(\theta)$$ | $$|\vec{F}_{wire}|=IBLsin(\theta)$$ | ||
- | {{ 184_notes: | + | [{{ 184_notes: |
- | where |$\vec{F}_{wire}$| is the magnitude of the force on the whole wire, I is the current through the wire, B is the // | + | where |$\vec{F}_{wire}$| is the magnitude of the force on the whole wire, $I$ is the current through the wire, $B$ is the // |
To find the direction of the magnetic force, we will need to use the [[184_notes: | To find the direction of the magnetic force, we will need to use the [[184_notes: |