Solution to UniPhysics_II_HW #5

# Solution to UniPhysics_II_HW #5 - Solution to - HW...

This preview shows pages 1–4. Sign up to view the full content.

Solution to -- HW assignment #5 Chapter 33: Magnetic field and force --------------------------------------------------------------------------------------------------------------- (wires are long) Solve: The magnetic field strength at point a is () 00 at a top bottom top bottom 7 0 at a 22 5 at a , out of page , into page 11 1 1 21 0 T m /A1 0 A 2 2.0 cm 4.0 2.0 cm 2.0 10 m 6.0 10 m 6.7 10 T, out of page II BBB dd I B B μμ ππ μ π −− ⎛⎞ =+ = + ⎜⎟ ⎝⎠ ⇒= = × ⇒=× rrr r × At points b and c, 4 at 2 , into page , into page 2.0 10 T, into page B =+= × r 5 at 3 , into page , out of page B = × r ---------------------------------------------------------------------------------------------------------------------------------- (wires are long) Solve: (a) The Biot-Savart law (Equation 33.6) for the magnetic field of a current segment s Δ r is 0 2 ˆ Is r B 4 r Δ × = r r where the unit vector points from current segment Δ s to the point, a distance r away, at which we want to evaluate the field. For the two linear segments of the wire, ˆ r s Δ r is in the same direction as so ˆ, r ˆ 0. sr Δ ×= r For the curved segment, s Δ r and are always perpendicular, so . ˆ r ˆ s rs Δ× =Δ r Thus 0 Is 2 4 B r Δ = Now we are ready to sum the magnetic field of all the segments at point P. For all segments on the arc, the distance to point P is r = R . The superposition of the fields is 0 4 I Bd s arc 44 L R RR μμθ == = where L = R θ is the length of the arc. (b) Substituting = 2 in the above expression loop center 2 42 B R R μπμ This is Equation 33.7, which is the magnetic field at the center of a 1-turn coil.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
---------------------------------------------------------------------------------------------------------------------------------- ( one can just use the formula ) 4 0 θ π μ r I B center = Visualize: Please refer to Figure P33.47. The distance from P to the inner arc is r 1 and the distance from P to the outer arc is r 2 . Solve: As given in Equation 33.6, the Biot-Savart law for a current carrying small segment s Δ r is 0 ˆ Is r B 2 r 4 Δ × = r r For the linear segm of the loop, B Δ s = 0 T because ents ˆ 0. sr Δ×= r Consider a segment s Δ r on length on the inner arc. Because s Δ r is perpendicular to the ˆ r vector, we have 2 00 BB 1 0 0 0 0 arc 1 22 11 1 1 1 1 2 44 4 4 4 4 Is I r I I d I I rr r r r r μμ ππ ΔΔΔ = = = = A similar expression applies fo == r arc 2 B . The right-hand rule indicates an out-of-page direction for B arc 2 and an into-page direction for B arc 1 . Thus, 0 , into page , out of page , into page 4 II I B r r 12 1 2 ⎛⎞ =+ = ⎜⎟ ⎝⎠ r The field strength is ( ) () 7 5 41 0 T m / A 5 . 0 A 7.9 10 T B × =− 4 0.010 m 0.020 m = × Thus B r = (7.9 × 10 T, into page). --- -------------------------------- –5 ---------------------------------------------------------------------------------- ------- -------------------------------- Visualize: Ampere’s integration paths are shown in the figure for the reg < r < R 1 , R 1 < r < R 2 , and R 2 r . < ions 0 m Solve: For the region 0 m < r < R 1 , 0 through Bds I ⋅= r r ú . Because the current inside the integration path is zero, B = 0 T. To find I through in the region R 1 < r < R 2 , we rrent density by the area inside the integration path that carries the current. Thus, multiply the cu I I through 1 21 rR RR
where the current density is the first term. Because the magnetic field has the same magnitude at every point on the circular path of

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/21/2011 for the course PHY 3240 taught by Professor Moore during the Spring '11 term at W. Florida.

### Page1 / 7

Solution to UniPhysics_II_HW #5 - Solution to - HW...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online