An elliptical cavity is carved within a perfect conductor. A positive charge q is placed at the centre of the cavity. The points A and B are on the cavity surface as shown in the figure.then
- electric field near A in the cavity = electric field near B in the cavity
- charge density at A = charge density at B
- potential at A = potential at B
- total electric field flux through the surface of the cavity is $q/ \varepsilon_0$
The Correct Option is D
Approach Solution - 1
Under electrostatic condition, all points lying on the conductor are at same potential. Therefore, potential at A = potential at B. Hence, option (c) is correct. From Gauss theorem, total flux through the surface of the cavity will be \(\frac{q}{\epsilon_0}\)
NOTE Instead of an elliptical cavity, if it would had been a spherical cavity then options (a) and (b) were also correct.
Approach Solution -2
Option D is correct. The total electric field flux passing through the surface of the cavity equals \(\frac{q}{\epsilon_0}\).
Under electrostatic conditions, all points on the conductor share the same potential. Hence, the potential at point A equals the potential at point B.
According to Gauss's theorem, the total flux passing through the surface of the cavity is \(\frac{q}{\epsilon_0}\).
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Concepts Used:
Electric charges and field
What is Electric Charge
It is the property of subatomic particles that experiences a force when put in an electric and magnetic field.
What is Electric Field
It is a 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 E, called electric field strength or electric field intensity.
Electric charges are of two types: Positive and Negative. It is commonly carried by charge carriers protons and electrons.
Properties of Electric Charge
Various properties of charge include the following :-
- Additivity of Electric Charge
- Conservation of Electric Charge
- Quantization of Electric Charge
Types of electric charge
Two kinds of electric charges are there :-
Negative Charge - When an object has a negative charge it means that it has more electrons than protons.
Positive Charge - When an object has a positive charge it means that it has more protons than electrons.
When there is an identical number of positive and negative charges, the negative and positive charges would cancel out each other and the object would become neutral.