Problem5 Consider a long, solid, cylindrical wire of radius a 3.1 mm. The current density J inside this wire points everywhere in the direction of the central axis of the wire. Its magnitude depends on the distance r from the central axis of the wire according to Tr where Jo is a constant. (a) What are the units of Jo? (b) Use Ampere's law to find an expression for the magnitude of the magnetic field B(r) inside the wire in terms of Jo, a, and r (c) Check your answer to part (b) by considering the following limits: (i) We expect the field at the center of the wire to be equal to zero. Why? Explain. Is the expression for the magnetic field you derived in part (b) consistent with this prediction? (i) We expect that B(r) will increase as Jo is increased. Why? Explain. Is the expression for the magnetic field you derived in part (b) consistent with this prediction? (ii) If we keep r fixed but increase the radius a of the wire, we expect the field at r to decrease. Why? Explain. Is the expression for the magnetic field you derived in part (b) consistent with this prediction?
Problem5 Consider a long, solid, cylindrical wire of radius a 3.1 mm. The current density J inside this wire points everywhere in the direction of the central axis of the wire. Its magnitude depends on the distance r from the central axis of the wire according to Tr where Jo is a constant. (a) What are the units of Jo? (b) Use Ampere's law to find an expression for the magnitude of the magnetic field B(r) inside the wire in terms of Jo, a, and r (c) Check your answer to part (b) by considering the following limits: (i) We expect the field at the center of the wire to be equal to zero. Why? Explain. Is the expression for the magnetic field you derived in part (b) consistent with this prediction? (i) We expect that B(r) will increase as Jo is increased. Why? Explain. Is the expression for the magnetic field you derived in part (b) consistent with this prediction? (ii) If we keep r fixed but increase the radius a of the wire, we expect the field at r to decrease. Why? Explain. Is the expression for the magnetic field you derived in part (b) consistent with this prediction?
Chapter12: Sources Of Magnetic Fields
Section: Chapter Questions
Problem 87AP: Magnetic field inside a torus. Consider a torus of rectangular cross-section with inner radius a and...
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Transcribed Image Text:Problem5
Consider a long, solid, cylindrical wire of radius a 3.1 mm. The current density J inside this wire
points everywhere in the direction of the central axis of the wire. Its magnitude depends on the
distance r from the central axis of the wire according to
Tr
where Jo is a constant.
(a) What are the units of Jo?
(b) Use Ampere's law to find an expression for the magnitude of the magnetic field B(r) inside the
wire in terms of Jo, a, and r
(c) Check your answer to part (b) by considering the following limits:
(i) We expect the field at the center of the wire to be equal to zero. Why? Explain. Is the
expression for the magnetic field you derived in part (b) consistent with this prediction?
(i) We expect that B(r) will increase as Jo is increased. Why? Explain. Is the expression for
the magnetic field you derived in part (b) consistent with this prediction?
(ii) If we keep r fixed but increase the radius a of the wire, we expect the field at r to decrease.
Why? Explain. Is the expression for the magnetic field you derived in part (b) consistent
with this prediction?
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