Force on a current carrying wire

[vorcil]

a)
A current‐carrying wire bent into a semicircle of radius r forms a close circuit as shown in the figure. A uniform magnetic field is directed normal to the linear section and in the plane of the loop. Show that the magnetic force acting on the closed wire loop is zero.
http://upload.wikimedia.org/wikipedia/commons/e/e9/Semicircle.svg

b)
List three items which operate on the principle “force acting on a current‐carrying conductor in a magnetic field”.

- n.b these aren't homework questions, I'm doing an experiment tomorrow and this was in a book I'm reading (related to the experiment)

I'm not sure how to solve the first one, can I do this mathematically? or is it more of a geometrical problem?

b - not sure if I know any practical applications of force on a current carrying wire,
All i can think of is the magneto in microwaves
anyone know any?

 

[vorcil]

http://upload.wikimedia.org/wikipedia/commons/e/e9/Semicircle.svg

 

[ideasrule]

b - not sure if I know any practical applications of force on a current carrying wire,
All i can think of is the magneto in microwaves
anyone know any?

I can think of two applications that are in your computer. You can probably hear one of them, and you listen to the other every day.

 

[Doc Al]

I'm not sure how to solve the first one, can I do this mathematically? or is it more of a geometrical problem?

How do you find the magnetic force on a current-carrying wire?

 

[vorcil]

How do you find the magnetic force on a current-carrying wire?

Use the lorentz force law,

Fmag = Q*(v*b)

then use the right hand rule, it says the magnetic field is into the semi circle, perpendicular to it's normal

not really sure how to solve it from here

 

[Doc Al]

Use the lorentz force law,

Fmag = Q*(v*b)

When dealing with a current, use:
$$\vec{F} = \vec{I}\ell \times \vec{B}$$

 

[vorcil]

how do i show that the magnetic force is 0 in the semicircle

http://upload.wikimedia.org/wikipedia/commons/e/e9/Semicircle.svg

 

[Doc Al]

how do i show that the magnetic force is 0 in the semicircle

What makes you think that the force on the semicircle is zero?

What's the force on the straight segment?

Hint: Find the force on an element of the semicircle, then integrate over the entire segment.

 

[vorcil]

What makes you think that the force on the semicircle is zero?

What's the force on the straight segment?

Hint: Find the force on an element of the semicircle, then integrate over the entire segment.

http://img529.imageshack.us/img529/6398/questionk.jpg

that's why i think it's 0, the question basically says it

-

would i get the circumference

(2*pi*r)/2 + (2r) = the length
= pi*r + 2r = total length of wire,

it's a closed loop with no apparent battery source

 

[Doc Al]

that's why i think it's 0, the question basically says it

There are two segments: the semicircular segment and the straight segment. The net force on the entire closed loop is zero. To show that, compute the force on each segment.