Circular Motion in a Magnetic Field Problem Help

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A charged particle moving perpendicular to a magnetic field experiences a magnetic force that causes it to move in a circular path, with the force's magnitude given by qvB. The problem involves demonstrating that momentum p equals qBr, even at speeds close to the speed of light, while noting that traditional force equations do not apply at relativistic speeds. The discussion emphasizes the importance of angular momentum, stating that if the charge does not radiate or collide, it maintains constant angular momentum. Participants are encouraged to consider how relativistic effects alter mass and the magnetic field in this context. Understanding these principles is crucial for solving the problem effectively.
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When a particle with electric charge q moves with speed v in a plane perpendicular to a magnetic field B, there is a magnetic force at right angles to the motion with magnitude qvB, and the particle moves in a circle of radius r. This formula for the magnetic force is correct even if the speed is comparable to the speed of light. Show that p = qBr even if velocity is comparible to c. Remember that F does not equal m*a at very high speeds.

Ive been working trying to solve this problem for several hours so I think I need some help. I've been trying to use the momentum principle, p(final) = p(initial) + F*t. Can anyone offer some help or advice?
 
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Why would one use "p(final) = p(initial) + F*t."

Think of angular momentum. If the charge does not radiate, nor collides with another particle, then it has constant angular momentum.

When a particle moves with a relativistic velocity, what correction is applied to the mass? What about the magnetic field?

Think about the formula for angular momentum.
 
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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