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Simon = Mc2
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Do you guys know of any physics experiment that I can do in my house? Please reply soon thanks.
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Physics Experiments to Do at Home
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Home physics experiments can be engaging and educational, with various resources available online. One suggested link provides a range of experiments suitable for different education levels, particularly junior high and above. Participants in the discussion express interest in sharing ideas and resources for conducting experiments at home. The conversation highlights the importance of accessibility and safety in home experimentation. Engaging in these activities can enhance understanding of physics concepts effectively.
Imagine a charged sphere at the origin connected through an open switch to a vertical grounded wire.
We wish to find an expression for the horizontal component of the electric field at a distance ##\mathbf{r}## from the sphere as it discharges.
By using the Lorenz gauge condition:
$$\nabla \cdot \mathbf{A} + \frac{1}{c^2}\frac{\partial \phi}{\partial t}=0\tag{1}$$
we find the following retarded solutions to the Maxwell equations
If we assume that...
Maxwell’s equations imply the following wave equation for the electric field
$$\nabla^2\mathbf{E}-\frac{1}{c^2}\frac{\partial^2\mathbf{E}}{\partial t^2}
= \frac{1}{\varepsilon_0}\nabla\rho+\mu_0\frac{\partial\mathbf J}{\partial t}.\tag{1}$$
I wonder if eqn.##(1)## can be split into the following transverse part
$$\nabla^2\mathbf{E}_T-\frac{1}{c^2}\frac{\partial^2\mathbf{E}_T}{\partial t^2}
= \mu_0\frac{\partial\mathbf{J}_T}{\partial t}\tag{2}$$
and longitudinal part...
The issue : Let me start by copying and pasting the relevant passage from the text, thanks to modern day methods of computing.
The trouble is, in equation (4.79), it completely ignores the partial derivative of ##q_i## with respect to time, i.e. it puts ##\partial q_i/\partial t=0##.
But ##q_i## is a dynamical variable of ##t##, or ##q_i(t)##. In the derivation of Hamilton's equations from the Hamiltonian, viz. ##H = p_i \dot q_i-L##, nowhere did we assume that ##\partial q_i/\partial...
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