Why is the electric field greater when equipotential lines are closer and relationship between magnetic field line spacing and field strength?
Ah, my friend Rk Naresh, let me unravel the mysteries of electric and magnetic fields for you Rk Naresh!
**Electric Field and Equipotential Lines:**
When equipotential lines are closer together, it signifies a more rapid change in potential. Electric field lines always run perpendicular to equipotential lines. Now, imagine traversing a shorter distance along these closely spaced equipotential lines. This means the change in potential occurs over a smaller distance. By the equation
E = -{dV}/{dr},
where E is the electric field, dV is the change in potential, and dr is the distance, you can see that a smaller dr results in a larger electric field. Therefore, the electric field is greater when equipotential lines are closer together.
**Magnetic Field Line Spacing and Field Strength:**
Magnetic field lines, on the other hand, form closed loops, unlike electric field lines. The density of magnetic field lines indicates the strength of the magnetic field. When the lines are more closely spaced, it means the magnetic field is stronger in that region.
Think of magnetic field lines as a bunch of threads. If you have many threads packed closely together, you have a strong, dense fabric. Similarly, closely spaced magnetic field lines indicate a strong magnetic field.
In a mathematical sense, the relationship is captured by Ampère's law for a closed loop, which states that the line integral of the magnetic field around a closed loop is equal to the product of the current passing through the loop and the permeability of free space. Mathematically,
B=μ0I/2πr,
where B is the magnetic field, mu0 is the permeability of free space, I is the current, and r is the distance from the wire.
So, to sum it up, closer spacing of magnetic field lines indicates a higher field strength, just like the closely spaced equipotential lines indicate a higher electric field.
Dear Rk Naresh,
both equipotential lines and magnetic field line spacing depends on the simulator or a person making drawing. The number of field lines can be any. Without a scale nothing can be said on the field strength. But as in an answer by Kaushik Shandilya typically more lines or closely spaced lines indicate stronger fields than less lines or sparsely spaced lines in a purely relative manner.
Regards,
Adam Abramowicz
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