Nene

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

29-2. A coil of wire 30 cm indiameter 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]; A = 7.07 x 10-2 m2; Δφ = φf - φo
[pic]
[pic]
Δφ = φf - φo = 36.7 mWb – 42.4 mWb; Δφ = -5.68 mWb

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 throughthe 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 (; BA = (0.5 T)(8.4 x 10-3 m2) = 4.2 x 10-3 T m2
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;
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. Aflux 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]; A = 4.52 x 10-2 m2; φ = BA sin (
[pic] ; B = 0.300 T

29-5. A magnetic flux of 50 (Wb passes through a perpendicular loop of wire having an area of 0.78 m2. What is the magnetic flux density?
[pic] ;B = 64.1 (T

29-6. A rectangular loop 25 x 15 cm is oriented so that its plane makes an angle ( with a 0.6-T B field. What is the angle ( 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]; ( = 41.80

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 directedupward. 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?
F = qvB( = (1.6 x 10-19 C)(2 x 106 m/s)(0.4 T)
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 velocityis directed at an angle of 350 with the magnetic flux? [ q = 2 (1.6 x 10-19 C) = 3.2 x 10-19 C ]
F = qvB sin( = (3.2 x 10-19 C)(3.6 x 106 m/s)(0.12 T) sin 350; F = 7.93 x 10-14 N

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 andthe direction the velocity v?
In order for the force to be INTO the paper for a NEGATIVE
charge, the 600 angle must be S of E. ( = 600 S of E
[pic]; B = 46.3 (T

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

29-11. What if an electron replaces the proton in Problem 29-10. What is the magnitude and direction of the magnetic force?
The direction of the magnetic force on an electron is opposite to that of the proton, but the magnitude of the force is unchanged since the magnitude of the charge is the same.Fe = 2.56 x 10-13 N, out of paper.
*29-12. A particle having a charge q and a mass m is projected into a B field directed into the paper. If the particle has a velocity v, show that it will be deflected into a circular path of radius:
[pic]
Draw a diagram of the motion, assuming a positive charge entering the B field from left to right. Hint: The magnetic force provides the necessary...