In a circular region, there is a uniform magnetic field B pointing into the page (Fig. 29-56). An xy coordinate system has its origin at the circular region's center. A free positive point charge +Q = 1.0 μC is initially at rest at a position x = +10 cm on the x axis. If the magnitude of the magnetic field is now INCREASED at a rate of 0.10 T/s, what force (magnitude and direction) will act on +Q?

Is B constant in magnitude for points that lie on a magnetic field line?

If a charged particle moves in a straight line, can you conclude that there is no magnetic field present?

Two long coaxial copper tubes, each of length L, are connected to a battery of voltage V. The inner tube has inner radius o and outer radius b, and the outer tube has inner radius c and outer radius d. The tubes are then disconnected from the battery and rotated in the same direction at angular speed of radians per second about their common axis. Find the magnetic field (a) at a point inside the space enclosed by the inner tube r d. (Hint: Hunk of copper tubes as a capacitor and find the charge density based on the voltage applied, Q=VC, C=20LIn(c/b) .)

Check Your Understanding In what orientation would a magnetic dipole have to be to produce (a) a maximum torque in a magnetic field? (b) A maximum energy of the dipole?

Consider an electron rotating in a circular orbit of radius r. Show that the magnitudes of the magnetic dipole moment and the angular momentum L of the electron are related by: = L=e2m

When the current through a circular loop is 6.0 A, the magnetic field at its center is 2.0104 T. What is the radius of the loop?

A 5.0-m section of a long, straight wire carries a current of 10 A while in a uniform magnetic field of magnitude 8.0103T . Calculate the magnitude of the force on the section if the angle between the field and the direction of the current is (a) 45°; (b) 90°; (C) 0°; or (d) 180°.

Check Your Understanding A uniform magnetic field of magnitude 1.5 T is directed horizontally from west to east, (a) What is the magnetic force on a proton at the instant when it is moving vertically downward in the field with a speed of 4 x 107 m/s? (b) Compare this force with the weight w of a proton.

A proton (charge +e, mass mp), a deuteron (charge +e, mass 2mp), and an alpha particle (charge +2e, mass 4mp) are accelerated from rest through a common potential difference V. Each of the particles enters a uniform magnetic field B, with its velocity in a direction perpendicular to B. The proton moves in a circular path of radius p. In terms of p, determine (a) the radius rd of the circular orbit for the deuteron and (b) the radius r for the alpha particle.