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When a coil makes a complete turn, why is does magnetic flux double with respect to time?

EMF, $\mathcal{E}$, is equal to -d($\phi$)/dt Where $\phi$ is magnetic flux. Why is it that if from $t_1$ to $t_2$ the coil makes a complete turn and during this turn the normal vector's angle with ...
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Do I need to differentiate this equation or not?

I've been given this equation: $$\mathrm{velocity}, v = 2\,\mathrm{cm/s^3} \,t^2 + 5\,\rm cm/s.$$ If someone now asks me to tell the velocity at, say 4 sec, then before proceeding with the equation, ...
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Units of the derivative of a function

I have a function $\phi(\mu, \sigma)$. $\mu$ and $\sigma$ are voltages (in mV in my case), so $\phi$ is a function of two voltages. $\phi$ itself, however, is in units of time (ms in my case). (...
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Would condensed matter physicists need more than three dimensional calculus? [closed]

The difference between "multivariable" and "vector" calculus, as stated on Yale's website, is that multivariable would only go through 2 or 3 dimensions, and so would rely heavily on geometric ...
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Expanding Electric Field, Magnetic Field in post-Newtonian Gravitational Potential

I've cross-posted this question from Mathematics since Physics is probably better suited for the nature of the question. I've ...
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Calculating Trajectory in non-Uniform electric field? [duplicate]

Above is the equation of the electric field. Where k is the electric constant, q is the charge on the particle and m is the mass of particle. The particle q initial position is (0,10) and starts off ...
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How do we calculate instantaneous velocity in 2D?

Suppose a body is moving with a constant speed of $10~\mathrm{ms^{-1}}$ in negative $x$ direction in $x$-$y$ plane. Let $\vec r$ be the position vector. Then what will be the instantaneous velocity ...
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Falling rain drop problem

I've been trying to solve this physics problem today "Spherical raindrop falls through a cloud with uniform density. After falling 1km it has a radius of 5mm. What volume fraction of the cloud is made ...
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Why is the elemental volume of a sphere equal to $4 \pi r^2dr$?

I was doing this question on calculating the electric field at a certain point in a sphere (length $r$ away from the centre), where the charge density is given by an equation. When I checked the ...
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Very basic question. Please show where I'm wrong in the following reasoning. The movement of an object in function of time could be described as $$x(t) = v t + x_{i}$$ if velocity is constant. If ...
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Optimization of Bottle Rocket Water Level

My (entry-level) physics class is building bottle rockets, and we are competing to build the longest-flying bottle rocket. The rockets are filled partway (we get to decide how much to fill them) with ...
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Derivation of Jefimenko's Equation in Jackson's EMT book

I have been trying to understand the derivation of Jefimenko's equation in Jackson on p.246-247 which can be seen in the photographs attached. First of all I did not fully comprehend the ...
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Differential operators in curvilinear coordinates

In the appendix A of Griffith's Electrodynamics text, he cites Spivak's Calculus on Manifolds as a reference more a more complete treatment of taking the gradient, curl, divergence, and Laplacian in ...
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Simplifying a Vector Integral

This question has (long) remained unanswered on MSE. While reading the book - Theory and Applications of Boltzmann Transport Equation by Cercignani, I found this integral which I am unable to ...
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What is the physical cause that circulation on a closed surface is zero?

This is quoted from Feynman's Lectures: We would like to see what happens when the loop shrinks down to a point, so that surface boundary disappears - the surface becomes closed. Now, if the ...
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Confusion regarding area from graph

This might be a trivial question but is illustrated below. Why is the area 'below' the graph always taken for a velocity-time graph when finding the displacement? I mean why is the area with the time ...
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Why is $\int_{s} \mathbf{h}\cdot \mathbf{n} da = - \dfrac{dQ}{dt}$ & not $\int_{s} \mathbf{h} \cdot\mathbf{n} da = - \dfrac{dQ}{dt} .{dt}$?

I was reading the Lectures of Feynman about surface integral where a situation in which heat is conserved has been dealt. Let there be $Q$ heat energy present inside a body. Now, if there is net heat ...
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Insight into Torricelli's Equation ($v^2=u^2+2as$) [closed]

Torricelli's Equation ($v^2=u^2+2as$) is usually presented as the particular formulation of the SUVAT system which doesn't involve t. It is derived from the others using some (perhaps well-motivated) ...
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Using differentials to optimize a function [closed]

I've read in a paper by Tevian Dray an alternative way to solve optimization problems manipulating "differentials". Here is an example of how it works (next I quote the paper). Consider the ...
435 views

$v^2 = 2ax$ or $v^2 = ax$?

As far as I am aware, $v^2 = 2ax$ is the formula to find the velocity in various questions. If kinetic energy = work, $$\frac{1}{2}mv^2=Fx$$ $$mv^2=2max$$ $$v^2=2ax$$ We use this formula to solve ...
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Problem in understanding the process of calculating the rotational inertia

As we know, rotational inertia is the mass-equivalent in rotation. For a discrete body, it is measured as $$I = \sum m_i{r_i}^2$$ . But when a continuous body comes, $$I = \int r^2 .dm$$ which ...
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Problem in deducing the equations of motion using indefinite integral

As we know, antiderivative or indefinite integral is the function the derivative of which gives the actual function. Let $F(x)$ be the derivative of $f(x)$ ie. the instantaneous rate of change of \$f(...
Zee in his book, Quantum field in a nutshell mentioned the following, p. 22: Equation (14): $$Z=\int{D\phi}e^{i\int d^4x{ {\frac{1}{2}[(\partial \phi)^2-m^2\phi^2]+J\phi}} }$$ He said then, ...