# Tag Info

Accepted

### Why is this vector field curl-free?

The vector $\hat \varphi$ is not defined at the origin, because the coordinate transformation $$(x,y) \mapsto (r,\varphi) = \left(\sqrt{x^2 + y^2}, \arctan(y/x)\right)$$ is singular there. Hence your ...
• 14.8k

### Why is this vector field curl-free?

There already are very good answers so I would just like to give some physical intuition why this vector field is curl-free even though it has non zero circulation. We can make an analogy of the curl ...
• 17.7k

### Why is this vector field curl-free?

That formula is valid outside the wire, where $J=0$. Maxwell 's equation says that $\nabla \times B = 0$ there. However there is no scalar field whose gradient is $B$ around the wire. This is the ...
• 71.7k

### Are the field lines on a bar magnet diagram contour lines?

No, the field lines are not contours. Contours usually connect places of equal magnitude, height, for example, on a map of a hill. The field lines on the diagram aren't connecting places of equal ...
• 13.7k
Accepted

### Why does the electric field have non-zero curl for magnetic monopoles?

With the standard caveat that all theory is predicated on experimental validation, I would strongly expect magnetic charge to obey a continuity equation. If you make the modifications you suggest ...
• 69.1k

### Why is this vector field curl-free?

OP's magnetic field $$\vec{B}~=~\frac{k }{\rho}\hat{\boldsymbol \varphi}, \qquad \rho~\neq~ 0,\tag{1}$$ in cylindrical coordinates $(\rho,\varphi,z)$ obeys (in a distributional sense) Ampere's ...
• 202k
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• 18.9k
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### Metals and Magnets

Newton's Third Law tells us that if object A exerts a force on object B then object B will exert an equal and opposite force on object A (this is required by the principle of conservation of momentum)....
• 53.2k
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### Is Biot-Savart Law valid for time-varying currents unlike Ampere's law?

The Biot Savart law is equivalent to Ampere's law without the Maxwell term under the assumption that the charge density has no time dependence. So if we have the usual situation where there are ...
• 8,700
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• 2,256

### What are the possible magnetic fields with constant magnitude?

Partial answer: if there are no currents, all such magnetic fields must be constant. In the absence of currents, we have $$\nabla \cdot \mathbf{B} = 0, \quad \nabla \times \mathbf{B} = 0.$$ The curl-...
• 102k
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### What exactly is enclosed current?

You have highlighted the fact that you can choose *any (well belaved) surface as long as it is bounded by the Amperian loop which means that \$\displaystyle \mu_0 \iint_{S_1} \mathbf{J} \cdot d\mathbf{...
• 96.2k

### Shouldn’t the magnetic field of a solenoid be affected by length?

The field at the center does depend on the total number of turns, but that is only relevant for a solenoid of finite length. Meanwhile, Ampère's Law only applies to a solenoid of infinite length. ...
• 2,423