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Question: A system has two charges \({q_A} = 2 \cdot 5 \times {10^{ - 7}}C\) and \({q_B} = - 2 \cdot 5 \times ...

A system has two charges qA=2⋅5×10−7C{q_A} = 2 \cdot 5 \times {10^{ - 7}}C and qB=−2⋅5×10−7C{q_B} = - 2 \cdot 5 \times {10^{ - 7}}C located at points A: (0,0,15cm) and B: (0,0,15cm) respectively. What is the total charge and electric dipole moment of the system?

Explanation

Solution

To solve this question, we have to understand the dipole moment for the second part of the question. To solve the first part of the question, we have to understand the fact that charges can be added like masses and are a scalar quantity.

Complete step by step solution:
There are two parts in the given problem.

Step 1: Calculating net charge.
The electric charge is the most fundamental physical property of matter that makes it experience a force when placed in the vicinity of another charge. There are two kinds of charges: positive and negative.
The charge is similar to the quantity mass. As masses of individual bodies can be added up without considering their direction, similarly, the charges can be added in a simple addition method.

In this case, the system contains two charges mainly, qA=2⋅5×10−7C{q_A} = 2 \cdot 5 \times {10^{ - 7}}C and qB=−2⋅5×10−7C{q_B} = - 2 \cdot 5 \times {10^{ - 7}}C.

The net charge in the system,

Q=q1+q2Q = {q_1} + {q_2}
Q=2⋅5×10−7+(−2⋅5×10−7)Q = 2 \cdot 5 \times {10^{ - 7}} + \left( { - 2 \cdot 5 \times {{10}^{ - 7}}} \right)
⇒Q=2⋅5×10−7−2⋅5×10−7=0C\Rightarrow Q = 2 \cdot 5 \times {10^{ - 7}} - 2 \cdot 5 \times {10^{ - 7}} = 0C

Therefore, the net charge in the system is zero.

Step 2: Calculating electric dipole.
The electric dipole is a system of two charges of equal magnitude but opposite in nature, separated by a finite distance. The overall polarity of the dipole is represented by the quantity called dipole moment.
The dipole moment is equal to the product of the magnitude of the charge and distance of separation between them.

P=qdP = qd

Since the charges are placed at (0,0,15) and (0,0,15) , the charges are placed on the top of each other. The distance of separation between them is zero, d = 0.

Dipole moment, P = 0

Hence, the total charge and dipole moment of the system is equal to zero.

Note: The solubility of a compound in water is dependent on the quantity dipole moment. Molecules with significant dipole moment are called polar compounds and dissolve in water. Water itself is a polar compound, thereby making it a universal solvent.