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Q21P

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Fundamentals Of Physics
Found in: Page 680

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Short Answer

An isolated conductor has net charge+10×10-6 C and a cavity with a particle of charge=+3.0×10-6 C What is the charge on (a) the cavity wall and (b) the outer surface?

a) The charge on the cavity wall is-3.0×10-6 C .

b) The charge on the outer surface is +1.3×10-6 C .

See the step by step solution

Step by Step Solution

Step 1: The given data

a) Net charge on the isolated conductor,qiso =+10×10-6 C

b) Particle charge in the cavity,+3.0×10-6 C

Step 2: Understanding the concept of Gauss law

Using the concept of Gaussian surface, the net charge enclosed in a body is zero and thus, it can be defined by the electric flux passing through the enclosed volume of the surface.

Step 3: a) Calculation of the charge on the cavity wall

Consider a Gaussian surface that is completely within the conductor and surrounds the cavity. Since the electric field is zero everywhere on the surface, the net charge it encloses is zero. The net charge is the sum of the charge q in the cavity and the charge q(w) on the cavity wall,

Thus, the value of the charge on the cavity wall is given as follows:

q+qw =0 qw=-q qw=-3.0×10-6 C

Hence, the value of the charge is-3.0×10-6 C

Step 4: b) Calculation of the charge on the outer surface

The net charge Q of the conductor is the sum of the charge on the cavity wall and the charge qs on the outer surface of the conductor.

Thus, the value of the charge on the outer surface is given as:

Q=qw+qsqs=Q-qwqs=10×10-6 C--3.0×10-6 Cqs=+1.3×10-5 C

Hence, the value of the charge is+1.3×10-5 C

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