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en/9.1.1.md
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| ### Statement | |||
| − | $9.1.1.$ A force of 15 | ||
| + | $9.1.1.$ A force of $15 \mathrm{~N}$ acts on a linear conductor of length $10\mathrm{~cm}$, located perpendicular to a magnetic field, if the current in the conductor is $1.5\mathrm{~A}$. Find the induction of the magnetic field. | ||
| ### Solution | |||
| We find the Ampere force as $$ \vec{F} = (\vec{Il})\times \vec{B} $$ In scalar form, this expression can be rewritten as $$ F = B\cdot Il \cdot \sin\alpha\tag{1} $$ since the field is perpendicular to the current element, then $$ \alpha =90^{\circ};\quad \sin\alpha =1 $$ From here, we rewrite the expression $(1)$ as $$ F = B \cdot Il \Rightarrow \boxed{B = \frac{F}{Il} = 100\text{ T}} $$ | |||
| #### Answer | |||
| $$B = \frac{F}{Il} = 100\text{ T}$$ | |||
| unchanged lines 5 | |||
| @@ -1,6 +1,6 @@ | |||
| ### Statement | ### Statement | ||
| $9.1.1.$ A force of 15 |
$9.1.1.$ A force of $15 \mathrm{~N}$ acts on a linear conductor of length $10\mathrm{~cm}$, located perpendicular to a magnetic field, if the current in the conductor is $1.5\mathrm{~A}$. Find the induction of the magnetic field. | ||
| ### Solution | ### Solution | ||
| We find the Ampere force as $$ \vec{F} = (\vec{Il})\times \vec{B} $$ In scalar form, this expression can be rewritten as $$ F = B\cdot Il \cdot \sin\alpha\tag{1} $$ since the field is perpendicular to the current element, then $$ \alpha =90^{\circ};\quad \sin\alpha =1 $$ From here, we rewrite the expression $(1)$ as $$ F = B \cdot Il \Rightarrow \boxed{B = \frac{F}{Il} = 100\text{ T}} $$ | We find the Ampere force as $$ \vec{F} = (\vec{Il})\times \vec{B} $$ In scalar form, this expression can be rewritten as $$ F = B\cdot Il \cdot \sin\alpha\tag{1} $$ since the field is perpendicular to the current element, then $$ \alpha =90^{\circ};\quad \sin\alpha =1 $$ From here, we rewrite the expression $(1)$ as $$ F = B \cdot Il \Rightarrow \boxed{B = \frac{F}{Il} = 100\text{ T}} $$ | ||
| #### Answer | #### Answer | ||
| $$B = \frac{F}{Il} = 100\text{ T}$$ | $$B = \frac{F}{Il} = 100\text{ T}$$ | ||
| unchanged lines 5 | |||