3. The N and S pole faces of a bent cylinder magnet form are separated from one another by a small gap, forming the magnetic analogue of a parallel plate capacitor. Positive magnetic charge is uniformly distributed on the north pole face and negative magnetic charge is uniformly distributed on the south pole face. If the magnetic field B in the gap is 0.2 Tesla, what is the magnetic surface charge density on each of the two pole faces? If the radius of the pole faces is 4.0 cm, what is the force of attraction between them?

2. Two very long straight wires (treat as infinite) carry currents in the direction shown. a. Draw arrows (or write or ) for the magnetic field at point P due to (i) the current I and (ii) the current 31. b. Determine the magnitude of the magnetic field at point P. I 2L L I 31

5. A long cylindrical conductor of radius R carries a current I. The current density is non- uniform, and is a function of the radius according to J = br, where b is a constant. Find an expression for the magnetic field for both rR (i.e. inside and outside the conductor). Assume that R is measured from the center of the conductor.

HW10.7. Field due to current segment A 15.5 A current flows through the wire shown in the figure. Take x = y B = X P What is the magnitude of the magnetic field due to a 0.20 mm segment of wire as measured at point P? number (rtol=0.03, atol=0) 4.60 cm and y 1.20 cm. T

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2. A small square loop of side length a carries a clockwise current I and is placed within a non-uniform magnetic field described by the expression B = (x² + y²) 2. a. Calculate the direction and magnitude of the total force on the loop. To find the force on each segment, evaluate the integral of Idix B by integrating along x or y in the direction of current flow. Then add the four segment forces together to find the total force. b. Calculate the magnetic dipole moment of the loop. Does a ○ B(x,y) X the loop experience a torque from the magnetic field? C. Where in the xy-plane would the potential energy be at a minimum? Does the force calculated in (a) move the loop toward this location or away from this location?

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Physics 6. A loop of area 0.250 m2 is in a uniform 0.020 0-T magnetic field. If the flux through the loop is 3.8310-3 T·m2, what angle does the normal to the plane of the loop make with the direction of the magnetic field?

A small circular coil of 20 loops of wire having a radius of 1 cm is at rest in the X-y plane (so the normal to the loop points in the +z-direction). A uniform magnetic field of 0.5 T is turned on in the +x-direction. What is the magnetic flux through the loop? a. 7.85 x 10 Tm² b. 1.57 x 10 4 T m² O c. 3.14 x 10 3 T m2 O d. 0 T m2

The aurora is caused when electrons and protons, moving in the earth’s magnetic field of  ≈5.0×10^−5 T, collide with molecules of the atmosphere and cause them to glow. a.  What is the frequency of the circular orbit for an electron with speed 1.0×10^6 m/s? Assume that the electron moves in a plane perpendicular to the magnetic field. b.  What is the frequency of the circular orbit for a proton with speed 5.0×10^4 m/s?