Physics Class 12 NCERT Solutions: Chapter 2 Electrostatic Potential and Capacitance Part 10 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Formula of Electric Potential

Q: 22. Figure shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole, obtain the dependence of potential on r for , and contrast your results with that due to an electric dipole, and an electric monopole (i.e.. , a single charge) .

Q_22_1_Electric Dipole, and an Electric Monopole

Answer:

Four charges of same magnitude are placed at points , and respectively, as shown in the following figure.

Q_22_2_The Four Charges of Same Magnitude

A point is located at P, which is r distance away from point Y.

The system of charges forms an electric quadrupole.

It can be considered that the system of the electric quadrupole has three charges.

Charge placed at point X

Charge placed at point

Charge placed at point

Electrostatic potential caused by the system of three charges at point P is given by,

Since ,

is taken as negligible.

It can be inferred that potential,

However, it is known that for a dipole,

And, for a monopole,

Q: 23. An electrical technician requires a capacitance of in a circuit across a potential difference of . A large number of capacitors are available to him each of which can withstand a potential difference of not more than . Suggest a possible arrangement that requires the minimum number of capacitors.

Answer:

Total required capacitance,

Potential difference,

Capacitance of each capacitor,

Each capacitor can withstand a potential difference,

Suppose a number of capacitors are connected in series and these series circuits are connected in parallel (row) to each other. The potential difference across each row must be and potential difference across each capacitor must be . Hence, number of capacitors in each row is given as

Hence, there are three capacitors in each row.

Capacitance of each row

Let there are n rows, each having three capacitors, which are connected in parallel.

Hence, equivalent capacitance of the circuit is given as

However, capacitance of the circuit is given as .

Hence, rows of three capacitors are present in the circuit. A minimum of i.e.. , capacitors are required for the given arrangement.

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