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Fundamentals Of Physics
Found in: Page 684

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Short Answer

The net electric flux through each face of a die (singular of dice) has a magnitude in units of 103 Nm2/C that is exactly equal to the number of spots N on the face (1 through 6). The flux is inward for N odd and outward for N even. What is the net charge inside the die?

The net charge inside the die is 2.66×10-8 C .

See the step by step solution

Step by Step Solution

Step 1: Listing the given quantities

  • The net electric flux = 103 N.m2/C

Step 2: Understanding the concept of Gauss law

Gauss law describes the relation between charge and electric field in a static situation. The equation for Gauss law is,


Here, qencis the net charge inside an imaginary closed surface and is the net flux of the electric field through the surface.

Step 3: Net charge inside the die

Let 0=103 N.m2/C.

The net flux through the entire surface of the dice is given by:

=n-16Φn =n-16(-1)nnϕ0 =ϕ0(-1+2-3+4-5+6) =3ϕ0

Thus, the net charge enclosed is:

role="math" localid="1657360360230" q=ε0ϕ =3ε0ϕ0 =38.85×10-12 C2/N.m2103 N.m2/C =2.66×10-8 C

Therefore, the net charge inside the die is =2.66×10-8 C .

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