Q. 73

# Find the magnitude of the electric field at the point P in the configuration shown in figure for d >> a. Take 2qa = p.

Answer :

**Given:**(a)

Distance between charge and P : d

(b)

Distance between two charges +q and -q = 2a

Dipole moment : p =2qa

**Formula used:**

(a)

It’s a direct formula of the electric field due to a point charge:

Here, k is a constant and k= =9× 10

^{9}Nm

^{2}C

^{-2}. q is the point charge and d is the distance between the charge and the point P

(b)

For the second configuration too we have a direct formula.

Opposite charges at both ends separated by a distance forms a dipole and electric field at a point on the perpendicular bisector of the dipole is given as:

Here, p is the dipole moment and is : p= 2qa and k is a constant and k= =9× 10

^{9}Nm

^{2}C

^{-2}, d is the distance between Point P and the center of the dipole.

(c)

Figure (c) is made up of combination of system in (a) and (b)

Point P is influenced by two dipoles.

1.-q and +q (A and B)

2. +q and +q (B and C)

1. Is the result of (b) = E

_{2}

2. Is the result of (a) = E

_{1}

Hence net electric field at P in the configuration (c) would be resultant of E

_{1}and E

_{2}

Hence, results for (a), (b) and (c) are **,** **,** and respectively.

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