Name: Electric and Gravitational Forces
Uploaded: 2019-07-19
Duration: 3 min 11 s
Description: Do you know the difference and similarities between the gravitational force and electrostatic force? Watch this video to explore it. Don't miss it.

Question

Two point charges

+ q

and

- q

are placed distance d apart. What are the points at which the resultant electric field is parallel to the line joining the two charges?

Accepted Answer

As shown in Fig. suppose the charges $+ q$ and $- q$ are located at points $A$ and $B$ distance $d$ apart.

Let $P$ be a point such that $A P = r_{1}$ and $B P = r_{2}$

Electric field at P due to charge $+ q$ is

$E_{1} = \frac{1}{4 π ε_{0}} \cdot \frac{q}{r_{1}^{2}}$

along $A P$ produced.

Electric field at $P$ due to charge $- q$ is

$E_{2} = \frac{1}{4 π ε_{0}} \cdot \frac{q}{r_{2}^{2}}$

along PB produced.

Draw $P R ∥ A B$ and $P Q, P S ⊥ P R$ . If $α$ and $β$ are the angles made by $A P$ and $B P$ with $A B$ , then

Component of $E_{1}$ along $P R = E_{1} \cos α$

Component of $E_{1}$ along $P Q = E_{1} \sin α$

Component of $E_{2}$ along $P R = E_{2} \cos β$

Component of $E_{2}$ along $P S = E_{2} \sin β$

The resultant field will be parallel to $P R$ if the components $E_{1} \sin α$ and $E_{2} \sin β$ are equal and opposite or each component is zero. Hence

(i) When $E_{1} \sin α = E_{2} \sin β$

$\frac{1}{4 π ε_{0}} \frac{q}{r_{1}^{2}} \cdot \frac{P S}{r_{1}} = \frac{1}{4 π ε_{0}} \cdot \frac{q}{r_{2}^{2}} \times \frac{P S}{r_{2}}$

or

$r_{1} = r_{2}$

(ii) When $E_{1} \sin α = E_{2} \sin β = 0$ , we have

$\sin α = \sin β = 0$

i.e., $α = 0^{\circ}$ or $180 °$ and $β = 0$ and $180 °$

Thus the resultant intensity will be parallel to the line joining $A$ and $B$ if (i) $P$ lies on the perpendicular bisector of $A B$ , or (ii) $P$ lies on either side of $A B$ i.e., $α = 0 °$ and $β = 180^{\circ}$ .

Two point charges $+ q$ and $- q$ are placed distance d apart. What are the points at which the resultant electric field is parallel to the line joining the two charges?

Important Questions on Electric Charges and Field

Learn and Prepare for any exam you want !

Two point charges +q and -q are placed distance d apart. What are the points at which the resultant electric field is parallel to the line joining the two charges?

Important Questions on Electric Charges and Field

Learn and Prepare for any exam you want !

Two point charges $+ q$ and $- q$ are placed distance d apart. What are the points at which the resultant electric field is parallel to the line joining the two charges?