Two charges +10 microcoulomb and -10 microcoulomb are placed 5 mm apart. Determine the electric field at a point P on the axis of the dipole 15 cm away from its centre O on the side of the positive charge
Answers
Wonderful Question.
Electric field due to an dipole ⇒ Dipole creates its own electric field in each and every possible direction.
Now, If it is asked at the axis of the dipole, then the formula which you will use to calculate the electric filed at an point P along the axis is given by,
E = 2kp/r³
where r is the distance from the centre of the dipole.
[Note this formula is valid only when r >>>>>> a, where a is the half of the dipole distance.]
Since, 15 cm is not much less than 5/2 = 2.5 mm.Thus, we can't use this formula.
Correct formula will be,
E = 2kpr/(r² - a²)⁴
Now, p = dipole moment
= magnitude of charge × distance between charges.
= 10 × 10⁻⁶ × 5 × 10⁻³
= 5 × 10⁻⁸ Cm.
a (distance between charges and centre of dipole) = 5/2 = 2.5 mm
= 2.5 × 10⁻³ m.
r = 15 cm. = 0.15 m.
Thus, E = 2 × 9 × 10⁹ × 5 × 10⁻⁸ × 0.15/(0.15² - 0.005²)⁴
E = 135/(0.15² - 0.005²)⁴
E = 5.29 × 10⁸ N/C.
Hope it helps.
Explanation:
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