Question
Derive an expression for the electric field due to the system of point charges?
✓
Answer
Electric field due to the system of point charges:
Suppose a number of point charges are distributed in space. To find the electric field at some point P due to this collection of point charges, the superposition principle is used. The electric field at an arbitrary point due to a collection of point charges is simply equal to the vector sum of the electric fields created by the individual point charges. This is called the superposition of electric fields.
Consider a collection of point charges $q_1, q_2, q_3, \ldots, q_n$ located at various points in space. The 'total electric field at some point $P$ due to all these $n$ charges is given by
Here $r_{1 p}, r_{2 p}, r_{3 p}, \ldots, r_{n p}$ are the distance of the charges $1, q_2, q_3, \ldots, q_n$ from the point respectively. Also $\hat{r}_{1 p}+\hat{r}_{2 p}+\hat{r}_{3 p}, \ldots, \hat{r}_{ np }$ are the corresponding unit vectors directed from $q_1, q_2, q_3, \ldots, q_n$ tpo $P$.
Equation (2) can be re-written as,
For example in figure, the resultant electric field due to three point charges $q_1, q_2, q_3$ at point $P$ is shown. Note that the relative lengths of the electric field vectors for the charges depend on relative distantes of the charges to the point $P$.
Suppose a number of point charges are distributed in space. To find the electric field at some point P due to this collection of point charges, the superposition principle is used. The electric field at an arbitrary point due to a collection of point charges is simply equal to the vector sum of the electric fields created by the individual point charges. This is called the superposition of electric fields.
Consider a collection of point charges $q_1, q_2, q_3, \ldots, q_n$ located at various points in space. The 'total electric field at some point $P$ due to all these $n$ charges is given by
Here $r_{1 p}, r_{2 p}, r_{3 p}, \ldots, r_{n p}$ are the distance of the charges $1, q_2, q_3, \ldots, q_n$ from the point respectively. Also $\hat{r}_{1 p}+\hat{r}_{2 p}+\hat{r}_{3 p}, \ldots, \hat{r}_{ np }$ are the corresponding unit vectors directed from $q_1, q_2, q_3, \ldots, q_n$ tpo $P$.
Equation (2) can be re-written as,
For example in figure, the resultant electric field due to three point charges $q_1, q_2, q_3$ at point $P$ is shown. Note that the relative lengths of the electric field vectors for the charges depend on relative distantes of the charges to the point $P$.
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