A very long insulating cylinder of charge of radius 2.50 cm carries a uniform linear density of

step 1 Welcome to problem number twenty three. Twenty two. Chapter twenty three. Electric potential. So

A very long insulating cylinder of charge of radius 2.50 cm...

Key Concepts

Electric Potential and Field Relationship

The electric potential difference between two points is defined as the negative line integral of the electric field between those points. This relationship is fundamental because it connects the easy-to-compute electric field (using Gauss's law or other methods) to the electric potential, which is often measured in experiments.

Integration of the Electric Field

Integrating the electric field along a path provides the potential difference between two points. In problems with radial symmetry, the integration is simplified by aligning the path with the direction in which the field is constant, making it possible to derive relationships between distances and voltage differences in the system.

Gauss's Law

Gauss's law relates the net electric flux through a closed surface to the charge enclosed within that surface. It is especially useful in finding electric fields in situations with significant symmetry, as it simplifies the calculation by reducing complex integrations into algebraic equations based on the symmetry of the charge distribution.

Cylindrical Symmetry

Cylindrical symmetry applies to systems where the charge distribution remains invariant under rotations around and translations along an axis. Recognizing cylindrical symmetry allows one to choose an appropriate Gaussian surface (a cylinder) such that the electric field is constant over parts of the surface, further simplifying the application of Gauss's law.

Transcript

00:01 Welcome to problem number twenty three.

00:02 Twenty two.

00:03 Chapter twenty three.

00:04 Electric potential.

00:06 So we have given that there is a long insulating slender here and this gettys leading the charge density, which is lambda here and the values fifteen nano column permata so nano eastenders on minus nine.

00:22 So this becomes fifteen tennis.

00:24 Mann ist ein code number terry, this is given we have two point five centimeters.

00:29 So which means that you're open to it to five meters.

00:34 This is a very small radios.

00:36 So this charge is supposed to charge.

00:38 That means whatever the charge besides from this road is just forced to charge toe.

00:46 Let's make some forty charge here.

00:52 So the question says, if we measure the potential difference between a point from this point, that's what we have when some and from the surface and under point is on the surface.

01:06 So the potential difference using putting world amida we should have won seventy five wood.

01:12 So this is a potential difference between this point and the surface point.

01:18 So we have a formal here, which we will use to find out the the distance.

01:25 So d prime mister distance from our sentinel drone so this is the point where the devil is one seventy five in respect of the surface point and a prime is a point from the centre of the road.

01:41 So this is handed off the so therefore deep time minus r.

01:46 Is it cause to do so? this is what we have to find out.

01:49 So we need to find out.

01:55 So these the point from the surface point from the surface.

02:05 So we will calculate this d or the plane first using this formula.

02:14 So that is your call, sir lam going to biopsy logarithms barbie r v is the distance from the centre of the road to the point and are these the centre are is also did some distance from the centre of the road to some other point.

02:32 So let's say we have a here and be here, so these have distance from the center.

02:46 So we know that the prime is the distance from the road and art is also the radius, which means the ideas is from the center of the world towards the surface.

02:57 So we will use this formula to find out the value d prime and then we can finally be.

03:06 So this becomes gotta be it caused too.

03:17 Our a explain intial to buy absolute then gov over lambda to just taking out the terms of the left inside.

03:38 So we have let's solve this equations.

03:41 We have our vehicles too.

03:43 You exponential dubai.

03:47 Absolutely love you, amanda.

03:50 So we know the potential difference between surface and this point which way have to find on a distance.

03:58 So we will use this ari as the surface here...