An electric dipole consists of charges q and -q separated by...

An electric dipole consists of charges $q$ and $-q$ separated by a distance $3 R .$ The dipole lies on the negative $x$ axis and is moving in the positive $x$ direction as shown in Figure $17.60 .$ The dipole passes through a sphere of radius $R$ centered at the origin. Make a sketch of the electric flux through the sphere as a function of time.

Key Concepts

Gauss's Law

Gauss's Law is a fundamental principle in electromagnetism that relates the electric flux through a closed surface to the net charge enclosed by that surface. It states that the total flux equals the enclosed charge divided by the permittivity of free space. This law is pivotal in problems involving symmetry and in understanding how the configuration of charges influences the electric field distribution.

Time-Dependent Behavior of Enclosed Charge

When charges move relative to a fixed surface, the amount of charge enclosed by the surface can change over time, leading to variations in the electric flux. Understanding the dynamic entry and exit of charges from a region is crucial for analyzing transient electric behaviors and for sketching time-dependent flux curves as the configuration of enclosed charges changes.

Electric Dipole

An electric dipole consists of two oppositely charged particles separated by a distance. This configuration creates a characteristic electric field pattern with a directional dependence and a magnitude that decreases with distance. The concept is essential for understanding how the orientation and movement of charges affect the resulting electric field in space.

Electric Flux

Electric flux quantifies the amount of electric field passing through a given surface. It is calculated by taking the surface integral of the electric field over that surface. This measure is critical in linking field strength and the geometry of the surface, and it forms the basis for analyzing how the field interacts with material boundaries.

Transcript

00:01 Hi in the given problem here there is a stair having a radius 2r and along its diameter there is an electric dipole having a charge minus q and plus q and plus q whose length is 3r and radius of this sphere is r so the diameter here will be 2r.

00:53 This dipole will enter into this sphere and then moving with the same velocity v it will leave this sphere on the opposite side.

01:07 Means right hand side then we have to draw the graphical variation we have to draw the variation of magnetic or electric flux linked with this sphere with the passage of time for which we draw the axis exactly matching with this sphere like this so first of all, when this plus q charge will enter here into the sphere, the electric flux will start linking through this sphere and it keeps on linking through the sphere up to a time taken by the sphere to move, taken by the positive q charge to move from left end of this horizontal diameter to its right end.

02:14 And here we are representing the time here and here it will be flux electric flux so to find this time first of all time taken by the positive due charge to move inside the sphere from left and the right end of its horizontal diameter will be time even equals to distance upon speed distance here it will be equal to the diameter length of diameter divided by speed v and electric flux linked to the surface by by by by plus 1 upon epsilon 0 times the charge and close.

03:54 The flux is positive as it is coming out of this sphere.

03:58 So we can mark this time here to here, even, which is equal to twice of r by v.

04:18 And the flux remains constant like this.

04:37 And the value of this constant flux is q by epsilon not.

04:43 Now when this plus q charge has moved a distance of 2r within the sphere, the remaining length is r only.

04:54 So when this plus q will start coming out of this sphere towards right -hand side, minus q charge has not entered into the sphere, still it is out.

05:05 So, now the flux will become zero.

05:08 Flux link through the sphere will become zero.

05:10 And it will remain zero until the negative q charge enters into the sphere...

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