What is the magnitude of the current density across A1 ?

[zooropa]

Homework Statement

The figure represents a section of a circular conductor of nonuniform diameter carrying a current of 5.00 A. The radius of cross-section A1 is 0.400 cm.
[URL=http://img97.imageshack.us/i/img01mn.jpg/][PLAIN]http://img97.imageshack.us/img97/7220/img01mn.th.jpg[/URL][/PLAIN]

Homework Equations

(a) What is the magnitude of the current density across A1 ?
(b) If the current density across A2 is one-fourth the value across A1, what is the radius of the conductor
at A2 ?

The Attempt at a Solution

J=I/A= 5.00A/pi(.004)^2=99,472.8 A m^2
Could someone help please? I am doing this the right way?

 

[berkeman]

Homework Statement

The figure represents a section of a circular conductor of nonuniform diameter carrying a current of 5.00 A. The radius of cross-section A1 is 0.400 cm.
[URL=http://img97.imageshack.us/i/img01mn.jpg/][PLAIN]http://img97.imageshack.us/img97/7220/img01mn.th.jpg[/URL][/PLAIN]

Homework Equations

(a) What is the magnitude of the current density across A1 ?
(b) If the current density across A2 is one-fourth the value across A1, what is the radius of the conductor
at A2 ?

The Attempt at a Solution

J=I/A= 5.00A/pi(.004)^2=99,472.8 A m^2
Could someone help please? I am doing this the right way?

Looks correct so far, except for the units of your answer -- should be A/m^2. You did the right thing in the division, just left out the "/" in the final answer's units.

 

[kerimek]

As a scientist, it is important to use the correct units for calculations. In this case, the units for current density are A/m^2, not A m^2. Therefore, the correct calculation would be J=I/A= 5.00A/(pi*0.004m)^2= 99,472.8 A/m^2. This means that the magnitude of the current density across A1 is 99,472.8 A/m^2.

To find the radius of the conductor at A2, we can use the fact that the current density across A2 is one-fourth the value across A1. Therefore, the current density at A2 would be 99,472.8 A/m^2 divided by 4, which is 24,868.2 A/m^2. We can use the same formula for current density, J=I/A, and solve for the radius at A2. This gives us A=I/J= 5.00A/24,868.2 A/m^2= 0.000201 m or 0.0201 cm. This is the radius of the conductor at A2.