Magnetism and the Electric Field

Chapter 29.  Magnetism and the Electric Field

Magnetic Fields

29-1.        The area of a rectangular loop is 200 cm2 and the plane of the loop makes an angle of 410 with a 0.28-T magnetic field.  What is the magnetic flux penetrating the loop?  

A = 200 cm2 = 0.0200 m2;     θ = 410;    B = 0.280 T[pic 1]

φ = BA sin θ = (0.280 T)(0.0200 m2) sin 410;      φ = 3.67 mWb

[pic 2]

29-2.        A coil of wire 30 cm in diameter is perpendicular to a 0.6-T magnetic field. If the coil turns so that it makes an angle of 600 with the field, what is the change in flux?

[pic 3];     A = 7.07 x 10-2 m2;     Δφ = φf - φo

[pic 4]

[pic 5][pic 6]

Δφ = φf - φo = 36.7 mWb – 42.4 mWb;      Δφ = -5.68 mWb

[pic 7]

29-3.        A constant horizontal field of 0.5 T pierces a rectangular loop 120 mm long and 70 mm wide.  Determine the magnetic flux through the loop when its plane makes the following angles with the B field: 00, 300, 600, and 900.    [Area = 0.12 m)(0.07 m) = 8.40 x 10-3 m2 ]

φ = BA sin θ;     BA = (0.5 T)(8.4 x 10-3 m2) = 4.2 x 10-3 T m2[pic 8][pic 9]

        φ1 = (4.2 x 10-3 T m2) sin 00 =   0 Wb;        φ2 = (4.2 x 10-3 T m2) sin 300 =  2.10 mWb;[pic 10][pic 11]

        φ3 = (4.2 x 10-3 T m2) sin 600 =  3.64 mWb;        φ1 = (4.2 x 10-3 T m2) sin 900 =  4.20 mWb

29-4.        A flux of 13.6 mWb penetrates a coil of wire 240 mm in diameter.  Find the magnitude of the magnetic flux density if the plane of the coil is perpendicular to the field.

[pic 12];     A = 4.52 x 10-2 m2;      φ = BA sin θ

[pic 13] ;     B = 0.300 T[pic 14]

[pic 15]

29-5.        A magnetic flux of 50 μWb passes through a perpendicular loop of wire having an area of 0.78 m2. What is the magnetic flux density?

[pic 16] ;          B = 64.1 μT[pic 17]

[pic 18]

29-6.        A rectangular loop 25 x 15 cm is oriented so that its plane makes an angle θ with a 0.6-T B field.  What is the angle θ if the magnetic flux linking the loop is 0.015 Wb?

A = (0.25 m)(0.15 m) = 0.0375 m2;      φ = 0.015 Wb

[pic 19];      θ = 41.80[pic 20]

The Force on  Moving Charge

29-7.        A proton (q = +1.6 x 10-19 C) is injected to the right into a B field of 0.4 T directed upward. If the velocity of the proton is 2 x 106 m/s, what are the magnitude and direction of the magnetic force on the proton?[pic 21]

        F = qvB⊥ = (1.6 x 10-19 C)(2 x 106 m/s)(0.4 T)[pic 22]

                        F = 1.28 x 10-13 N, into paper

29-8.        An alpha particle (+2e) is projected with a velocity of 3.6 x 106 m/s into a 0.12-T magnetic field.  What is the magnetic force on the charge at the instant its velocity is directed at an angle of 350 with the magnetic flux?   [ q = 2 (1.6 x 10-19 C) = 3.2 x 10-19 C ][pic 23]

F = qvB sinθ = (3.2 x 10-19 C)(3.6 x 106 m/s)(0.12 T) sin 350;    F = 7.93 x 10-14 N

[pic 24]

29-9.        An electron moves with a velocity of 5 x 105 m/s at an angle of 600 with an eastward B field.  The electron experiences an force of 3.2 x 10-18 N directed into the paper. What are the magnitude of B and the direction the velocity v?[pic 25]

        In order for the force to be INTO the paper for a NEGATIVE[pic 26]

        charge, the 600 angle must be S of E.     θ = 600 S of E

[pic 27];       B = 46.3 μT[pic 28]

[pic 29]

29-10.        A proton (+1e) is moving vertically upward  with a velocity of 4 x 106 m/s.  It passes through a 0.4-T magnetic field directed to the right. What are the magnitude and direction of the magnetic force?    [pic 30]

                [pic 31];    [pic 32]

                             F = 2.56 x 10-13 N, directed into paper.

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