SATHEE: Shortcut Methods

JEE Main & JEE Advanced:

1. Numerical on Lenz’s law:

Calculate the magnetic force acting on the rod: $$F_B = BIL$$ $$F_B = (0.5 T)(1 m)(100 g)(9.8 m/s^2) = 4.9 N$$
Use the right-hand rule to determine the direction of the induced current. The thumb points in the direction of motion, the fingers point in the direction of the magnetic field, and the middle finger points in the direction of the induced current. In this case, the induced current flows from the left rail to the right rail.

2. Numerical on motional emf:

Calculate the area of the loop: $$A = l\times w = (10 cm)(20 cm) = 200 cm^2$$ $$A = 0.02 m^2$$
Calculate the magnetic flux through the loop: $$\Phi = BAcos\theta$$ $$\Phi = (0.2 T)(0.02 m^2)cos0\degree$$ $$\Phi = 0.004 Wb$$
Calculate the induced emf: $$emf = -\frac{d\Phi}{dt}$$ $$emf = -\frac{(0.004 Wb- 0 Wb)}{1s- 0s}$$ $$emf = 4 mV$$

3. Numerical on Faraday’s law:

Calculate the change in magnetic flux through the solenoid: $$\Delta\Phi = NI(\Delta t)$$ $$\Delta\Phi = (1000 turns)(5 A)(0.1s)$$ $$\Delta\Phi = 50 Wb$$
Calculate the induced emf: $$emf = -\frac{d\Phi}{dt}$$ $$emf = -\frac{(50 Wb -0 Wb)}{(0.1s)- 0s}$$ $$emf = 500 V$$

4. Numerical on transformer action:

Calculate the turns ratio of the transformer: $$\frac{N_p}{N_s} = \frac{V_p}{V_s}$$ $$\frac{100 turns}{2000 turns} = \frac{12 V}{V_s}$$ $$V_s = \frac{(12 V)(2000 turns)}{100 turns}$$ $$V_s = 240 V$$

5. Numerical on self-inductance:

Calculate the induced emf: $$emf = L\frac{\Delta I}{\Delta t}$$ $$2 V = L\left(\frac{1 A - 0 A}{0.1 s -0 s}\right)$$ $$2 V = 10 L$$
Calculate the self-inductance: $$L = 0.2 H$$

1. Numerical on Lenz’s law:

Calculate the magnetic force acting on the rod: $$F_B = BIL$$ $$F_B = (0.5 T)(0.2 m)(5 m/s) = 0.5 N$$
Use the right-hand rule to determine the direction of the induced current. The thumb points in the direction of motion, the fingers point in the direction of the magnetic field, and the middle finger points in the direction of the induced current. In this case, the induced current flows from the bottom of the rod to the top of the rod.

2. Numerical on motional emf:

Calculate the area of the loop: $$A = l\times w = (5 cm)(10 cm) = 50 cm^2$$ $$A = 0.005 m^2$$
Calculate the magnetic flux through the loop: $$\Phi = BAcos\theta$$ $$\Phi = (0.1 T)(0.005 m^2)cos0\degree$$ $$\Phi = 0.0005 Wb$$
Calculate the induced emf: $$emf = -\frac{d\Phi}{dt}$$ $$emf = -\frac{(0.0005 Wb -0 Wb)}{1s - 0s}$$ $$emf = 0.5 mV$$

3. Numerical on Faraday’s law:

Calculate the change in magnetic flux through the solenoid: $$\Delta\Phi = NI(\Delta t)$$ $$\Delta\Phi = (500 turns)(2 A)(0.05s)$$ $$\Delta\Phi = 50 Wb$$
Calculate the induced emf: $$emf = -\frac{d\Phi}{dt}$$ $$emf = -\frac{(50 Wb - 0 Wb)}{0.05s -0 s}$$ $$emf = 1000 V$$

4. Numerical on transformer action:

Calculate the turns ratio of the transformer: $$\frac{N_p}{N_s} = \frac{V_p}{V_s}$$ $$\frac{500 turns}{100 turns} = \frac{220 V}{V_s}$$ $$V_s = \frac{(220 V)(100 turns)}{500 turns}$$ $$V_s = 44 V$$

5. Numerical on self-inductance:

Calculate the induced emf: $$emf = L\frac{\Delta I}{\Delta t}$$ $$1 V = L\left(\frac{0.5 A - 0 A}{0.05 s- 0 s}\right)$$ $$1 V = 10 L$$
Calculate the self-inductance: $$L = 0.1 H$$