PROBLEM 1. As shown in the figure, a uniform magnetic field B points upward, in the plane of the paper. Then the current is turned on in a long wire perpendicular to the paper. The magnetic field at point 1 is then found to be zero. From this information, draw the magnetic field vector at point 2 when the current is on. Draw the vector starting at the black dot. The location and orientation of the vector will be graded. The length of the vector will not be graded. Explain your reasoning. 2• 1. Wire

Three parallel wires each carry current I in the directions shown in the figure. (Figure 1) The separation between adjacent wires is d. Part A Calculate the magnitude of the net magnetic force per unit length on the top wire. Express your answer in terms of the variables I, d, and appropriate constants. Part B Calculate the magnitude of the net magnetic force per unit length on the middle wire. Express your answer in terms of the variables I, d, and appropriate constants. Part C Calculate the magnitude of the net magnetic force per unit length on the bottom wire. Express your answer in terms of the variables I, d, and appropriate constants.

Suppose that there is a magnetic field B Cartesian coordinate system with ê x ŷ = î. For all the discussions below, ignore the units. = 3xî filling a 3D space. The coordinates are set up as a a) Find the expression for the magnetic force on a positive charge +Q that is located at 7 = (2,1, –1) and moving at velocity i = (2,3,1) b) In this magnetic field, is it possible for any particle to move along a circular path? If so, indicate the conditions for the position and the velocity of the particle; If not, briefly explain your reasons.

A toroid is a solenoid bent into the shape of a doughnut. It looks similar to a toy Slinky® with ends joined to make a circle. Consider a toroid consisting of N turns of a single wire with current I flowing through it. (Figure 1) Consider the toroid to be lying in the re plane of a cylindrical coordinate system, with the z axis along the axis of the toroid (pointing out of the screen). Let represent the angular position around the toroid, and let r be the distance from the axis of the toroid. For now, treat the toroid as ideal; that is, ignore the component of the current in the direction. Figure 00 Ampèrean loop (a) 1 of 1 (b) Part A The magnitude of the magnetic field inside the toroid varies as a function of which parameters? ► View Available Hint(s) r only 0 only both r and Submit Part B Complete previous part(s) Part C Complete previous part(s) Part D In an ideal toroid, current would flow only in the and directions. The magnetic field in the central plane, outside of the coils of…