Answer to Question #181091 in Electricity and Magnetism for Ruby

Question

1. A straight wire carrying a 3.00-A current is placed in a uniform magnetic field of magnitude 0.280 T directed perpendicular to the wire. Find the magnitude of the magnetic force on a section of a wire having a length of 14.0 cm.
2. The magnetic field through a coil changes from 3 mT to 4.5 mT in 7 seconds. If the coil has 600 turns and a radius of 4 cm, what emf is induced in the coil?
3. A wire 12cm long and carrying a current of 30 A is placed in between the pole face of a magnet whose magnetic flux density is 0.9 T. If the wire is inclined at an angle of 60^o from the plane of the magnetic field, what is the force exerted on the wire?
4. A plane circular loop of conducting wire of radius 10 cm which possesses 15 turns is placed in a uniform magnetic field. The direction of the magnetic field makes an angle of 30 degrees with respect to the normal direction to the loop. The magnetic field-strength is increased at a constant rate from 1 T to 5T in a time interval of 10 s. What is the emf generated around the loop?

Answer 1

1. The magnetic force on the wire is , $F=ilB=3.0 \times 0.14 \times 0.28 =0.12 N$
2. $\epsilon =NA \frac{dB}{dt}=600 \pi \times (\frac{4}{100})^2 \times \frac{4.5-3}{7}=0.6463 mV$
3. The magnetic force , $F=ilBsin \theta=30 \times 0.12 \times 0.9 sin 60 = 2.8059 N$
4. $\epsilon =\frac{NA cos \theta (B_2-B_1)}{\triangle t}=\frac{15 \times \pi \times 10^{-2} cos 30 (5-1)}{10}=0.163 V$