First slide

Electric field

Question

Four electrical charges are arranged on the corners of a 10 cm square as shown. What would be the direction of the resulting electric field at the center point P?

Moderate

A

$\to$
B

$↑$
C

$\leftarrow$
D

$↓$

Solution

$E_{1} = E_{4} = 2 E_{2} = 2 E_{3}$
Resultant of $E_{4} a n d E_{2}$ is towards fourth charge.
Resultant of $E_{1} a n d E_{3}$ is towards third charge.
Now, horizontal components will be canceled, and net field will be upward. Angle between them =90 and $E n e t = 2 E \cos \frac{θ}{2} = 2 E \cos \frac{90}{2} = \sqrt{2} E u p w a r d s$

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