Given a current segment which flows along the edges of a cube as shown in the fi

Question

Given a current segment which flows along the edges of a cube as shown in the figure. The conventional Cartesian notation of ˆ? (a unit vector along the positive x axis), ˆk (a unit vector along the positive y axis), and ˆk (a unit vector along the positive z axis), is used. The cube has sides of length a. The current flows along the path A ? C ? D ? E ? G. There is a uniform magnetic field B~ = B j.

Find the magnitude F~magnetick the magnetic field exerts on the current segment ACDEG if the. Magnetic field is 4.92 T, a is 6.3 m, and the current is 5.91 A. Answer in units of N.

Explanation / Answer

Here,

as the magnetic force on a wire sagment is given as

F = iL X B

for the forces on wire ACDEG

as the direction of force on AC and EG will be oposite and will cancel out each other.

magnetic field , B = 4.92 T

a = 6.3 m

force on CD , FCD = 0 as both current and magnetic field in same direction

force on DE

FDE = B*I*a (-k)

FDE = 4.92 * 5.91 * 6.3

FDE = 183.2 N

the magnitude of net force acting on the current sagment is 183.2 N

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