Question regarding Magnetic field

AI Thread Summary
The discussion focuses on the transformation of electric and magnetic fields between two frames of reference in motion relative to each other. Participants clarify that 'c' refers to the speed of light and emphasize that the magnitudes of electric and magnetic fields can change due to Lorentz transformations in special relativity. The conversation highlights the importance of dimensional analysis in determining the correctness of the given equations. It is noted that the problem is more about understanding field transformations rather than complex magnetic concepts. Overall, the key takeaway is the necessity of applying special relativity principles to analyze the equations correctly.
utkarshakash
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Homework Statement


Let \vec{E} and \vec{B} denote electric and magnetic fields in a frame S and \vec{E'} and \vec{B'} in another frame S' moving with respect to S at a velocity \vec{v}. Two of the following equations are wrong. Identify them.

a)B_y ' = B_y + \dfrac{vE_z}{c^2}
b)E_y ' = E_y - \dfrac{vB_z}{c^2}
c)b_y ' = B_y + vE_z
d)E_y ' = E_y + vB_z

Homework Equations



The Attempt at a Solution


First of all I can't understand what is 'c' here. Is it speed of light?Also, how can the magnitude of field change with frame? The magnitude of force can vary but I don't think field should vary. This question seems too complicated to me.
 
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##c## is the speed of light yes. The magnetic and electric fields transform non-trivially under Lorentz boosts; one can prove this using special relativity. You can probably look it up online if you don't have a textbook that discusses it.
 
Dimensional analysis might be useful here.
 
jtbell said:
Dimensional analysis might be useful here.

Hmm... So its just basically a problem of dimensional analysis. No magnetics involved.
 
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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