The astronomical object 4U0142+61 has the distinction ofcreating the most powerf

Question

The astronomical object 4U0142+61 has the distinction ofcreating the most powerful magnetic field ever observed. Thisobject is referred to as a "magnetar" (a subclass of pulsars), andits magnetic field is 1.30E+15 times greater than the Earth'smagnetic field. Suppose a 1.77 m straight wire carrying a currentof 2.40 A is placed in this magnetic field at an angle of 66.9° to the field lines. 1. What force does this wire experience? 2. A field this strong can significantly change thebehavior of an atom. To see this, consider an electron moving witha speed of 2.62E+6 m/s. What is the maximum magnetic force exertedon the electron? 3. Calculate the ratio of this magnetic force to theelectric force a proton exerts on an electron in a hydrogen atom.The radius of the hydrogen atom is 5.29E-11 m. The astronomical object 4U0142+61 has the distinction ofcreating the most powerful magnetic field ever observed. Thisobject is referred to as a "magnetar" (a subclass of pulsars), andits magnetic field is 1.30E+15 times greater than the Earth'smagnetic field. Suppose a 1.77 m straight wire carrying a currentof 2.40 A is placed in this magnetic field at an angle of 66.9° to the field lines. 1. What force does this wire experience? 2. A field this strong can significantly change thebehavior of an atom. To see this, consider an electron moving witha speed of 2.62E+6 m/s. What is the maximum magnetic force exertedon the electron? 3. Calculate the ratio of this magnetic force to theelectric force a proton exerts on an electron in a hydrogen atom.The radius of the hydrogen atom is 5.29E-11 m.

Explanation / Answer

(a)   force = L I B sin = 1.77 * 2.40 * 5 x 10-5 * 1.30 x1015 * sin66.9 = .          =   2.54 x1011 N . (b) force = qvB = 1.60 x10-19 * 2.62 x 106 * 5 x10-5 * 1.30 x 1015 =  0.02725 N . (c) force of proton on electron = ke2 / r2 = 8.99 x 109 *(1.60 x 10-19)2 / (5.29 x 10-11)2   =
.                  =    8.2241 x 10-8 N . ratio =   0.02725 / 8.2241 x10-8   =      331300  

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