Name: Introduction to Electric Charge
Uploaded: 2019-07-19
Duration: 9 min 41 s
Description: In this video, we will study electric charge and its properties and we will also learn about different methods of charging.

Question

Explain the concept of electric field. Express electric flux through a surface in terms of electric field intensity. Show that the electric flux through a cylindrical surface with its axis parallel to a uniform electric field is zero.

Accepted Answer

Electric field, is an electric property associated with each point in space when charge is present in any form. The magnitude and direction of the electric field are expressed by the value of E, called electric field strength or electric field intensity or simply the electric field. The strength of an electric field at any point may be defined as the electric, or Coulomb, force exerted per unit positive electric charge q at that point, or simply. The strength of the electric field depends on the source charge, not on the test charge, provided that field is not disturbed by the presence of the test charge.

Given an electric field E the flux $△ ϕ$ through an element of surface ∆S is $△ ϕ = E . dS$

The cylindrical Gaussian surface has three parts, the two flat ends and the cylindrical surface. So you have the field entering end a at right angles to it, passing parallel to the cylindrical surface C, and then exiting end b again at right angles to it.

The corresponding flux through the curved surface would be zero since the outward pointing surface vector at all points on it would be perpendicular to the surface (and therefore the axis) while the field is parallel to the axis of the cylinder. Thus $ϕ_{C} = 0$

If the area of each of the flat ends is A, the contribution to the total flux at end $a$ would be $ϕ_{a} = - E . A$ (the negative sign arises because the surface vector A is outward and opposite to the field E ).

Similarly, the flux through end $b$ would be given by $ϕ_{b} = + E . A$ (the positive sign arises because the surface vector A is outward and in the same direction as the field E ).

Adding the three contributions we have

$ϕ = ϕ_{a} + ϕ_{b} + ϕ_{c} = \int_{a} E d S + \int_{b} E d S + \int_{c} E d S$

= $E d S \cos 0 ° + E d S \cos 180 ° + E d S \cos 90 ° = ES - ES + 0 = 0$

Explain the concept of electric field. Express electric flux through a surface in terms of electric field intensity. Show that the electric flux through a cylindrical surface with its axis parallel to a uniform electric field is zero.

Important Questions on Electric Charges and Fields

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