Question

You are holding a positive charge and there are positive charges of equal magnitude 1 m to your north and 1 m to your east. what is the direction of the force on the charge you are holding?

Answer 1

All these are positive charges. The force between them is the repulsive force.

The charge at the north is pushing your charge to the south, while the charge at the east is pushing it to the west.

The resultant force on the charge you are holding will be in the south-west direction because the other charges are of equal magnitude and direction from your charge.

Answer 2

see attachment,
Let I hold the a charge , q at the centre of given co-ordinate system.and two positive charge of equal magnitude Q are placed 1 m to my North and 1 m to my South .


now, both the charge are same nature e.g., positive . Let my charge is also positive { well, you can assume negative too , I am considering positive because it makes me easy to solve } then, both charge repel to my charge . { same nature charge repel each other }

charge Q placed on east is repelling my charge q toward west . similarly charge Q placed on North is repelling my charge q toward south .

now , use vector for solve it .
vector Fnet =vector Fe +vector Fn
$|F_{net} | = \sqrt{F_e^2+F_n^2}$
Fe = Fs = KqQ/(1m)² = KqQ
Fnet = √{Fe² + Fs²} = √{(kqQ)²+(KqQ)²}
Fnet = √2KqQ

hence, net force act on q {my charge } is √2KqQ and the direction of force is S - W direction .