13.1 Faraday’s law  (Page 3/6)

A stationary coil is in a magnetic field that is changing with time. Does the emf induced in the coil depend on the actual values of the magnetic field?

In Faraday’s experiments, what would be the advantage of using coils with many turns?

A copper ring and a wooden ring of the same dimensions are placed in magnetic fields so that there is the same change in magnetic flux through them. Compare the induced electric fields and currents in the rings.

Discuss the factors determining the induced emf in a closed loop of wire.

(a) Does the induced emf in a circuit depend on the resistance of the circuit? (b) Does the induced current depend on the resistance of the circuit?

How would changing the radius of loop D shown below affect its emf, assuming C and D are much closer together compared to their radii?

Can there be an induced emf in a circuit at an instant when the magnetic flux through the circuit is zero?

Does the induced emf always act to decrease the magnetic flux through a circuit?

How would you position a flat loop of wire in a changing magnetic field so that there is no induced emf in the loop?

The normal to the plane of a single-turn conducting loop is directed at an angle $\theta$ to a spatially uniform magnetic field $\overrightarrow{B}.$ It has a fixed area and orientation relative to the magnetic field. Show that the emf induced in the loop is given by $\epsilon =(dB\text{/}dt)(A\text{cos}\theta ),$ where A is the area of the loop.

A 50-turn coil has a diameter of 15 cm. The coil is placed in a spatially uniform magnetic field of magnitude 0.50 T so that the face of the coil and the magnetic field are perpendicular. Find the magnitude of the emf induced in the coil if the magnetic field is reduced to zero uniformly in (a) 0.10 s, (b) 1.0 s, and (c) 60 s.

Repeat your calculations of the preceding problem’s time of 0.1 s with the plane of the coil making an angle of (a) $30\text{°},$ (b) $60\text{°},$ and (c) $90\text{°}$ with the magnetic field.

A square loop whose sides are 6.0-cm long is made with copper wire of radius 1.0 mm. If a magnetic field perpendicular to the loop is changing at a rate of 5.0 mT/s, what is the current in the loop?

The magnetic field through a circular loop of radius 10.0 cm varies with time as shown below. The field is perpendicular to the loop. Plot the magnitude of the induced emf in the loop as a function of time.

The accompanying figure shows a single-turn rectangular coil that has a resistance of $2.0\text{Ω}.$ The magnetic field at all points inside the coil varies according to $B=B_0{e}^{\text{−}\alpha t},$ where $B_0=0.25\text{T}$ and $\alpha =200\text{Hz}.$ What is the current induced in the coil at (a) $t=0.001\text{s}$ , (b) 0.002 s, (c) 2.0 s?

How would the answers to the preceding problem change if the coil consisted of 20 closely spaced turns?

A long solenoid with $n=10$ turns per centimeter has a cross-sectional area of $5.0{\text{cm}}^2$ and carries a current of 0.25 A. A coil with five turns encircles the solenoid. When the current through the solenoid is turned off, it decreases to zero in 0.050 s. What is the average emf induced in the coil?

A rectangular wire loop with length a and width b lies in the xy -plane, as shown below. Within the loop there is a time-dependent magnetic field given by $\overrightarrow{B}(t)=C\left((x\text{cos}\omega t)\widehat{i}+(y\text{sin}\omega t)\widehat{k}\right)$ , with $\overrightarrow{B}(t)$ in tesla. Determine the emf induced in the loop as a function of time.

The magnetic field perpendicular to a single wire loop of diameter 10.0 cm decreases from 0.50 T to zero. The wire is made of copper and has a diameter of 2.0 mm and length 1.0 cm. How much charge moves through the wire while the field is changing?