A conducting wire frame is placed in a magnetic field which is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced current in wires AB and CD are :
in a circuit consisting of two loops connected in series (like a figure-eight), the larger loop effectively dictates the direction of the current for the entire circuit.
A coil resistance 20 Ω and inductance 5 H is connected with a 100 V battery. Energy stored in the coil will be :
Energy stored = 62.5 J
A square coil ACDE with its plane vertical is released from rest in a horizontal uniform
magnetic field B of length 2L. The acceleration of the coil is :
The acceleration is less than 'g' when entering or leaving the field because the changing magnetic flux induces a current that creates an opposing upward force (Lenz's Law).
Once the coil is fully inside the uniform 2L field, the flux is constant, the induced current drops to zero, and the coil falls freely with acceleration equal to g.
Two circular coils can be arranged in any of the three situations shown in the figure. Their
mutual inductance will be :
Based on the visual arrangement of the coils, the mutual inductance is maximum in situation (a).
This is because the coils are placed co-axially (one above the other), allowing the maximum amount of magnetic flux from the primary coil to pass through the secondary coil, resulting in the highest coupling coefficient.
A vertical bar magnet is dropped from position on the axis of a fixed metallic coil as shown in fig – I. In fig. II the magnet is fixed and horizontal coil is dropped. The acceleration of the magnet and coil are a1 and a2 respectively then
In both cases, relative motion between the magnet and the coil induces a current that creates a magnetic force opposing the motion (Lenz's Law). This upward retarding force reduces the downward acceleration below gravity ($g$), resulting in a_1 < g and a_2 < g.
Two identical coaxial circular loops carry a current i each circulating in the same direction. If the loops approach each other
When two loops with current in the same direction approach each other, the magnetic flux through each loop increases. According to Lenz's Law, an induced current will arise to oppose this change, causing the current in both loops to decrease.
Two coils X and Y are placed in a circuit such that a current changes by 2 A in coil X and the magnetic flux change of 0.4 Wb occurs in coil Y. The value of mutual inductance of coils is :
The mutual inductance ($M$) is calculated by the ratio of flux change in coil Y to the current change in coil X:
$M = 0.2 \text{ H}$
A small square loop of wire of side l is placed inside a large square loop of wire of side L ( L > l ). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to :
The mutual inductance M is found by calculating the magnetic flux through the small loop due to the current I in the large loop. Using the formula for the magnetic field at the center of a square loop, B \frac{I}{L}.
Since the small loop is much smaller than the large one \(L \gg l)\, the field is approximately uniform across its area \A = l^2\. The flux \Phi = B \cdot A$ is therefore proportional to \\frac{I}{L} \cdot l^2\.
Because $M = \frac{\Phi}{I}$, the mutual inductance scales as: