Concept #1: Magnetic Flux

Practice: A ring of radius 0.5m lies in the xy-plane. If a magnetic field of magnitude 2 T points at an angle of 22° above the x-axis, what is the magnetic flux through the ring?

Example #1: Magnetic Flux of a Rotating Ring

A circular coil with a 15 cm radius and 150 loops is oriented in the xy-plane. If a uniform 5 mT magnetic field is oriented 37o above the xy-plane, what is the magnetic flux through the coil?

A circular coil with 200 loops and a radius of 0.15 mm is placed 12 m from a straight, current-carrying wire as shown in the following figure. What is the magnetic flux through the coil? Assume that the magnetic field is roughly constant through the coil, since 12 m >> 0.15 mm.

A 2.0 m conductor is formed into a square and placed in the horizontal xy-plane. A magnetic field is oriented 30.0° above the horizontal with a strength of 3.0 T. What is the magnetic flux through the conductor?
A) 6.0 T • m2
B) 0.65 T • m2
C) 0.75 T • m2
D) 0.37 T • m2

Consider a circular loop of radius R in the presence of a uniform magnetic field. Which of the following statements is true?
A) Doubling the magnetic field would result in the same change in flux as doubling the radius would.
B) Doubling the angle between the magnetic field and the surface will double the magnetic flux.
C) Changing the angle between the axis of the coil and the field from 90o to some θ angle would result in the same change in flux as doubling the area of the coil.
D) Halving the radius of the coil halves the magnetic flux through the coil.
E) None of the above are true.

A circular coil with 150 loops and a radius of 10 cm is initially oriented in a 0.5 mT magnetic field, with the axis of the coil and the field at a 30o angle. After some time, the coil rotates so that the field is at an angle of 40o to the plane of the coil, and the field strength drops to 0.3 mT. What is the change in magnetic flux during this time?

A 2.0 m conductor is formed into a square and placed in the horizontal xy-plane. A magnetic field is oriented 30.0° above the horizontal xy-plane with a strength of 1.0 T. What is the magnetic flux through the conductor?A) 0.25 T•m2B) 0.12 T•m2C) 0.22 T•m2D) 2.0 T•m2

The trig. function of angle φ between vectors B and A in the magnetic flux should be (sine / cosine) __________

A conducting wire with a total length of 2.0 m is formed into a square and placed in the horizontal xy-plane. A magnetic field is oriented 30.0° above the horizontal with a strength of 10.0 T. What is the magnetic flux through the conductor?A) 2.5 T • m2B) 20 T • m2C) 1.2 T • m2D) 2.2 T • m2