Question

1. A straight vertical wire carries a current of 1.45 A downward in a region between the poles of a large electromagnet where the field strength is 0.585 T and is horizontal. a. What are the magnitude of the magnetic force on a 1.00 cm section of this wire if the magnetic-field direction is toward the east? b. What are the magnitude of the magnetic force on a 1.00 cm section of this wire if the magnetic-field direction is toward the south? c. What are the direction of the magnetic force on a 1.00 cm section of this wire if the magnetic-field direction is 30.0 o south of west ? d. What are the magnitude of the magnetic force on a 1.00 cm section of this wire if the magnetic-field direction is 30.0 o south of west ?

2. What is the speed of a beam of electrons when the simultaneous influence of an electric field of 1.54×10⁴ V/m and a magnetic field of 4.72×10⁻³ T , with both fields normal to the beam and to each other, produces no deflection of the electrons? b. When the electric field is removed, what is the radius of the electron orbit? c. What is the period of the orbit?

3. In a cloud chamber experiment, a proton enters a uniform 0.340 T magnetic field directed perpendicular to its motion. You measure the proton's path on a photograph and find that it follows a circular arc of radius 6.04 cm . How fast was the proton moving?

Answer 1

1)Given,

I = 1.45 A ; B = 0.585 T ;

a)l = 1 cm = 0.01 m

We know that, the magnetic force on a current carrying wire is:

F = B I L sin(theta)

F = 0.585 x 1.45 x 0.01 x sin90 = 8.5 x 10^-3 T

Hence, F = 8.5 x 10^-3 T

b)F = B I L sin(theta)

F = 0.585 x 1.45 x 0.01 x sin90 = 8.5 x 10^-3 T

Hence, F = 8.5 x 10^-3 T

c)F = B I L sin(theta)

B = -0.585 cos30 i - 0.585 sin30 j

B = -0.507 i - 0.293 j

L = -0.01 k

F = I (L x B)

F = 1.45 [(-0.01) x (-0.507 i - 0.293 j)] = -0.00425 i + 0.00735 j

F = sqrt (0.00425^2 + 0.00735^2) = 8.5 x 10^-3

Hence, F = 8.5 x 10^-3 T

d)theta = tan^-1 (-0.00425/0.00735) = -60 deg

Hence, theta = -60 deg