What are the solutions to questions regarding charging by induction, magnetic field patterns of a solenoid, and DC/AC circuits?

Here are the solutions to the questions:

15.

a) To charge an uncharged body positively by induction:

1. Bring a negatively charged body close to the uncharged body without touching it. This repels free electrons in the uncharged body to the far side, leaving the near side positively charged.
2. Ground the uncharged body while the negatively charged body is still nearby. The repelled electrons flow to the ground.
3. Remove the ground connection.
4. Remove the negatively charged body. The uncharged body is left with a net positive charge.

b) The magnetic field pattern around a current-carrying solenoid consists of:

• Uniform, parallel, and closely spaced field lines inside the solenoid, indicating a strong and uniform magnetic field.
• Field lines that emerge from one end (North pole) and curve around to enter the other end (South pole), resembling the field of a bar magnet.

c)

i) The two circuits are:

• Fig. I: A DC (Direct Current) circuit.
• Fig. II: An AC (Alternating Current) circuit.

ii) For the three components (resistor, inductor, capacitor) connected in series in Fig. II, the current flowing through each component is the same.

iii) To calculate the current in the circuit in Fig. I:

Step 1: Calculate the equivalent resistance of the parallel combinations.
For the two $2 \text{ Ω}$ resistors in parallel:

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