How Do You Calculate the Line Integral of a Magnetic Field Between Two Points?

AI Thread Summary
To calculate the line integral of a magnetic field (B) between two points, the relevant equation is ∫B ds = BL, where L represents the length of the path along which the integral is taken. The magnetic field around a straight wire carrying current is circular and perpendicular to the direction of the current. The direction of the differential path element (ds) must be considered in relation to the wire's magnetic field. Understanding the geometry of the situation is crucial for correctly applying the line integral. This approach will yield the desired result for the line integral of the magnetic field.
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Homework Statement



What is the line integral of B (vector) between points i and f in the figure?

knight_Figure_32_22.jpg



Homework Equations



?
∫B ds = BL ??

The Attempt at a Solution



What equation would I use for this?
 
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Notice that the wire is perpendicular to the "page" with the current running "into the page", that is, away from you. What does the magnetic field around this wire look like? How does ds point relative to the wire? What equation have you learned about that involved a line integral of B ds?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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