What Is the Magnetic Force on a 1-cm Segment of a Current-Carrying Wire?

[swankymotor16]

A rectangular loop of wire measures 1.0 m by 1.0 cm. If a 7.0-A current flows through the wire, what is the magnitude of the magnetic force on the centermost 1.0-cm segment of the 1.0-m side of the loop?


Fm = ILBsin of angle

Fm = Magnetic force

I= Electric current

L= Length of conductor

B= magnetic field intensity

B= (4∏x10^-7)(7.0A)/(2∏)(0.01m) = 1.4x10^-8


Fm= (7.0A)(1.0m)(1.4x10^-8)= 9.8x10_8

my final answer is 9.8X10^-8, IS THIS CORRECT? PLEASE HELP!

 

[collinsmark]

A rectangular loop of wire measures 1.0 m by 1.0 cm. If a 7.0-A current flows through the wire, what is the magnitude of the magnetic force on the centermost 1.0-cm segment of the 1.0-m side of the loop?Fm = ILBsin of angle

Fm = Magnetic force

I= Electric current

L= Length of conductor

B= magnetic field intensity

B= (4∏x10^-7)(7.0A)/(2∏)(0.01m) = 1.4x10^-8

(Don't forget your units.)

That's a pretty good approximation. The formula which you used for B, can be derived using Ampere's law (Edit: or you could use calculus + Biot-Savart law), is only really valid for an infinitely long wire. But since we're dealing with a distance to the wire being much, much shorter than the wire itself, it makes a fine approximation. (If you wanted to get more precise, you'd have some calculus to do. But I'm guessing the approximation is fine for this problem.)

Fm= (7.0A)(1.0m)(1.4x10^-8)= 9.8x10_8

my final answer is 9.8X10^-8, IS THIS CORRECT? PLEASE HELP!

(Again, don't forget your units.)

Hold on, the problem statement said,

"magnetic force on the centermost 1.0-cm segment"​

It's not asking for the force on the entire 1 meter wire. It's just asking for a force on the center-most 1 centimeter segment of the 1 m wire.