# Q 1.8(a): Two point charges  and  are located 20 cm apart in vacuum. (a) What is the electric field at the midpoint O of the line AB joining the two charges?

Given, AB = 20 cm

Since, O is the midpoint of the line AB.

AO = OB = 10 cm = 0.1m

The electric field at a point caused by charge q, is given as,

Where, q is the charge, r is the distance between the charges and the point O

k = 9x109 N m2 C-2

Now,

Due to charge at A, Electric field at O will be  and in the direction AO.

Similarly the Electric field at O due to charge at B,  also in the direction AO

Since, both the forces are acting in the same direction, we can add their magnitudes to get the net electric field at O:

E' =  +  = 2E (Since their magnitudes are same)

along the direction AO.

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