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Fundamentals Of Physics
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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,

ε0Φ=qenc

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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