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More on Solenoids Long solenoids have spatially uniform B inside (from Ampere’s law) If the current is increased linearly with time, the B field will increase linearly with time. In this case, the field is out of the page (top view) and increasing with time. If this is done, what will be the direction of the induced E field at point b, distance r from the axis? On the top view: A] up B] down C] left D] right E] out of the page

More on Solenoids Consider a loop at a radius r. The flux is upward and increasing, so the induced EMF must be such as to cause a downward B field if a loop of wire were there. So the EMF must be CW (from above) and E must point downward (top view.) Let’s do the math….

More on Solenoids What is the induced E field at point a, on the solenoid axis? A] 0 B] not zero

More on Solenoids What is the induced E field at point c, outside the solenoid, where B is essentially zero? A] 0 B] not zero, upward (top view) C] not zero, downward (top view) D] not zero, leftward(top view).c

Now consider 4 loops, all with the same area. The B field is increasing with time. What is true? A] loops a,b,c have the same , but d has less. B] loops a and c have  =0, but b and d have same nonzero . C] loop a has  =0, but b,c,d have the same, nonzero . D] loop c has  =0, loop a has a little, b has more, and d the most. E] loop c has  =0, but loops a,b,d all have the same nonzero .

Ampere’s law