Faraday's Experiments on Electromagnetic Induction

What this figure shows. A coil C of insulated wire is connected to a galvanometer G to form a closed circuit, with a bar magnet used to probe it in six panels. With the magnet outside and at rest, the galvanometer shows no deflection. As the magnet's north pole is pushed INTO the stationary coil, the galvanometer deflects momentarily to the right, showing a transient current. If the magnet is then held stationary inside the coil, the deflection returns to zero. Withdrawing the magnet produces a momentary deflection in the OPPOSITE (left) direction. Moving the magnet faster produces a LARGER deflection. Finally, reversing the magnet so its south pole faces the coil reverses every deflection obtained with the north pole. Together the six panels establish that a current appears only while there is RELATIVE MOTION between the magnet and the coil, that its direction depends on whether the magnet …

What this figure shows. Two separate circuits are placed near each other with no galvanic (wire) connection between them: a primary circuit made of a coil P, a battery B and a key K, and a secondary circuit made of a coil S and a galvanometer G. Panel (a) shows the key K being closed, so current in the primary circuit rises from zero to a steady value; at that moment the galvanometer in the SECONDARY circuit gives a momentary deflection to the right, even though the two coils share no direct electrical connection. Once the primary current settles to its steady value, the secondary galvanometer returns to zero. Panel (b) shows the key being opened, so the primary current falls from its steady value to zero; this again produces a momentary secondary deflection, but this time to the LEFT, opposite to panel (a)'s deflection. The experiment shows that a changing current in one coil, p …

What this figure shows. Two panels reinterpret Figure 4.2's first-experiment observations directly in terms of magnetic flux. Panel (a) shows the bar magnet and coil C approaching each other: the magnetic field lines threading the coil become denser ("magnetic flux linked is more"), so the flux through the coil is increasing, and the galvanometer shows a right deflection corresponding to this rising flux. Panel (b) shows the magnet and coil receding from each other: the field lines threading the coil become sparser ("magnetic flux linked is less"), so the flux is decreasing, and the galvanometer shows a left deflection. The figure makes explicit that it is not the magnet's motion by itself, but the resulting CHANGE IN FLUX linked with the coil, that is the true cause of the induced current, and …

What this figure shows. Three panels reinterpret Figure 4.3's second-experiment observations in terms of flux linked with the secondary coil S. Panel (a) shows the primary key open: no current flows in P, so no magnetic field is produced, and the flux linked with S is zero -- the galvanometer shows no deflection. Panel (b) shows the key just closed: the primary current is increasing, building up an increasing magnetic field around P, so the flux linked with S is increasing, inducing a transient current shown by a right galvanometer deflection. Panel (c) shows the key just opened: the primary current is decreasing, so the field -- and hence the flux linked with S -- is decreasing, inducing a transient current in the opposite sense, shown by a left deflection. Together the three panels confirm that it is always the rate of CHANGE of flux linked with …

Worked out. A cylindrical bar magnet is placed along the axis of a circular solenoid and rotated about that same axis, and the question asks whether any current is induced in the coil. Because a cylindrical magnet's field is perfectly symmetric about its own axis, rotating it about that axis does not change the pattern of field lines threading the solenoid at all -- the flux linked with the solenoid stays exactly constant throughout the rotation. Since Faraday's law requires a CHANGING flux to induce an emf, and here the flux never changes despite the visible motion, no current is induced in the solenoid at all. The example is a useful reminder that mechanical motion alone is not sufficient for induction; only m …

Worked out. A closed coil of 40 turns and area 200 cm$^2$ sits in a field of flux density 2 Wb/m$^2$ and is rotated in 0.2 s from a position where its plane makes $30^{\circ}$ with the field to a position where its plane is perpendicular to the field, and the induced emf is required. The initial angle between the field and the coil's NORMAL is $\theta_i = 90^{\circ}-30^{\circ}=60^{\circ}$, giving initial flux $\Phi_i = BA\cos60^{\circ} = (2)(200\times10^{-4})(0.5) = 2\times10^{-2}$ Wb; the final position (plane perpendicular to field) means the normal is ALONG the field, $\theta_f=0^{\circ}$, giving $\Phi_f = BA\cos0^{\circ} = (2)(200\times10^{-4})(1) = 4\times10^{-2}$ Wb. The induced emf is $\varepsilon = N\,\dfrac{\Delta\Phi_B}{\Delta t} = 40\times\dfrac{(4-2)\times10^{-2}}{0.2} = 40\times0.1 = 4$ V, showing how the flux …

Worked out. A straight conducting wire, oriented along the east-west direction, is dropped horizontally from a height, and the question asks whether an emf is induced in it. The wire moves vertically downward while Earth's magnetic field has a horizontal component pointing roughly north-south; since the wire's east-west length is perpendicular to both its own downward velocity AND to the horizontal component of Earth's field, the wire genuinely cuts across Earth's magnetic field lines as it falls. This is exactly the geometry of motional emf (developed formally in the next section via the Lorentz force), so the answer is yes -- an emf IS induced across the ends of the falling wire, even though there is no coil, no galvanometer, and no visible circuit anywhere in the problem, because the unde …