Question

A system has two charges $q_A=2.5\times {10}^{-7}C$ and $q_B=-2.5\times {10}^{-7}C$ is located at points $A(0,0,-15)cm$ and $B(0,0,+15cm)$ respectively. What is the total charge and electric dipole moment vector of the system?

Answer 1

Step 1. Given Data,

$q_A=2.5\times {10}^{-7}C$
$q_B=-2.5\times {10}^{-7}$

$A(0,0,-15cm)andB(0,0,+15cm)$

Step 2. Formula used,

Dipole moment= $P=q\times d$

$d$ is the length of the dipole

$q$ is the given charge

Step 3. Calculating the total charge,

The amount of charge at A, $q_A=2.5\times {10}^{-7}C$
The amount of charge at B, $q_B=-2.5\times {10}^{-7}$
The total charge of the system is $q=q_A+q_B=2.5\times {10}^{-7}C=0$

Hence the total charge is $0$.

Step 4. Calculating the electric dipole moment

Distance between points A and B,
$d=15+15=30cm=0.3m$

The electric dipole moment of the system,

$P=q_A\times d=2.5\times {10}^{-7}\times 0.3=7.5\times {10}^{-8}cm$ along the positive z-axis.
Hence, the electric dipole moment of the system is $7.5\times {10}^{-8}$ along the positive z-axis.