Magnetic Field and electric Field

AI Thread Summary
If a charged particle maintains constant velocity in a region with a zero external magnetic field, it cannot be concluded that the external electric field is also zero, as a nonzero electric field would exert a force and cause acceleration. Conversely, if the external electric field is zero, it does not imply that the external magnetic field is also zero; the particle could still experience a force due to a nonzero magnetic field, as described by the Lorentz force law. The discussion emphasizes the necessity of considering all forces acting on the particle to understand the relationship between electric and magnetic fields. Overall, the interplay between electric and magnetic fields is crucial for analyzing the motion of charged particles.
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Homework Statement



A charged particle, passing through a certain region of space,has a velocity whose magnitude and directions remain constant.

a. If it is known that the external magnetic field is zeroseverywhere in this region, can you conclude that the external electric field is also zero? Explain.

b. If it is known that the external electric field is zero everywhere, can you conclude that the external magnetic field isalso zero? Explain.


The Attempt at a Solution



This is more of a conceptual question, and I really have no idea how to approach it.
If someone could help clarify this, that would be great!

Thanks
 
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physicsdreams said:

Homework Statement



A charged particle, passing through a certain region of space,has a velocity whose magnitude and directions remain constant.

a. If it is known that the external magnetic field is zeroseverywhere in this region, can you conclude that the external electric field is also zero? Explain.

Well first of all I guess we have to assume that the particle doesn't experience any OTHER external forces, e.g. if it were confined to a wire or something. So from here on out I will assume the only forces possible are either electric or magnetic.

Suppose the electric field were nonzero. Then the charged particle would feel a force, and would thus experience some accelleration--i.e., its velocity's magnitude or direction would change.

b. If it is known that the external electric field is zero everywhere, can you conclude that the external magnetic field isalso zero? Explain.

This argument is slightly different. Remember the Lorentz force law : F = q(E+v x B). E is zero, so F = qv x B. Can this be zero for nonzero B?
 
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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