Q.Predict the direction of induced current in the situations described by the following Figs. 6.15(a) to (f).

Concept — Lenz's law: the induced current flows so as to oppose the change in magnetic flux that produces it. Coil by coil, decide whether the linked flux rises or falls, then pick the current sense that opposes it.

(a) The magnet approaches with its S-pole leading, so the flux linked with the coil increases; the near face must become a south pole to repel it → current is q $\to$ r $\to$ p $\to$ q (qrpq).

(b) For the left coil the N-pole recedes and for the right coil the S-pole approaches. Opposing each change gives p $\to$ r $\to$ q $\to$ p (prqp) in the left coil and y $\to$ z $\to$ x $\to$ y (yzxy) in the right coil.

(c) Closing the key makes the current, and hence the flux through the neighbouring coil, grow; the induced current opposes the rise → y $\to$ z $\to$ x $\to$ y (yzxy).

(d) Moving the rheostat contact changes the current and so the flux through the adjacent coil; the induced current opposes that change → z $\to$ y $\to$ x $\to$ z (zyxz).

(e) Opening the key makes the current, and the linked flux, collapse; the induced current tries to maintain it → x $\to$ r $\to$ y $\to$ x (xryx).

(f) No induced current. The field of the straight wire lies in the plane of the loop, so the flux through the loop is zero and stays zero even as the current changes.

Principle. The induced current always opposes the change in linked magnetic flux ($\varepsilon=-\,d\Phi_B/dt$). For each figure, decide whether the flux through the given coil is increasing or decreasing, then name the current sense that opposes that change.

(a) A bar magnet approaches the coil with its south pole leading. The linked flux increases, so the face of the coil towards the magnet must become a south pole to push it away. Tracing that current sense round the coil gives qrpq.

(b) A magnet lies between two coils and moves so that its N-pole recedes from the left coil while its S-pole approaches the right coil.

• Left coil: flux due to the receding N-pole decreases, so the induced current opposes the fall — this gives prqp.
• Right coil: flux due to the approaching S-pole increases, so the induced current opposes the rise — this gives yzxy.

(c) The tapping key in the primary circuit has just been closed, so its current, and the flux it sends through the neighbouring coil, is growing. The induced current opposes this increase, giving yzxy.

(d) The rheostat setting in one coil is being changed, altering its current and hence the flux linked with the adjacent coil. The induced current opposes that change and flows as zyxz.

(e) The tapping key has just been opened, so the primary current and the flux it linked collapse to zero. The induced current in the neighbouring coil tries to maintain that flux, giving xryx.

(f) A long straight wire carries a changing current, with a planar loop placed so that the wire's magnetic field lines lie in the plane of the loop. Because the field lines run along the plane of the loop instead of piercing it, they thread no area of the loop: the flux linked is zero at every instant. So even though the current changes, there is no change of flux and hence no induced current.

Method: Finding Induced-Current Direction When the Source of Flux Change Isn't a Moving Magnet

Many Lenz's-law figures don't show a magnet moving — the changing flux instead comes from a changing current in a neighbouring coil (a key being opened/closed, a rheostat being adjusted) or from a wire whose field simply doesn't link the loop at all. This method extends the basic "moving magnet" reasoning to those cases.

Steps

Step 1: Identify the actual source of the changing flux in each panel

Before applying Lenz's law, name what is changing: is a permanent magnet approaching/receding? Is a switched circuit's current rising (just closed) or falling (just opened)? Is a rheostat changing a circuit's current smoothly? Each of these changes the flux through a nearby coil via mutual induction, exactly like a moving magnet would.

Step 2: Decide whether the linked flux is increasing or decreasing

• Approaching magnet / just-closed key / rising rheostat current → flux increasing.
• Receding magnet / just-opened key / falling rheostat current → flux decreasing.

Step 3: Apply Lenz's law and the right-hand rule as usual

Increasing flux → induced current opposes it (creates an opposing field); decreasing flux → induced current tries to sustain it (creates a supporting field). Use the right-hand grip rule to convert that field direction into a current direction around the labelled loop.

Step 4: Check for the special case of zero linkage

If the field lines from a straight current-carrying wire lie in the plane of the nearby loop (rather than piercing through it), the flux threading the loop is zero at every instant — no matter how the current changes. Always check the geometry of how the field lines relate to the loop's plane before assuming a changing current must induce something.

This four-step diagnostic — name the source, judge the flux trend, apply Lenz's law, and check for zero-linkage geometry — covers every panel of a multi-part "determine the induced current" figure, whatever is doing the changing.