Question

What is the magnitude of the electric field at a point midway between a −6.5μC and a +8.2μC charge 8.4 cm apart? Assume no other charges are nearby. And what is the direction of the electric field?

Answer 1

According to the question, we need to find electric field at a point midway between -6.5 C and +8.2 C charge which are separated 8.4 cm apart. Assume that both the charges are placed along X-axis.

Thus, the distance of midpoint where electric field is to be found out from both the charges will be 4.2 cm.

Hence, we have charges q_{​​​​​​1}​​​ = -6.5 C = -6.5 × 10^-6 C and q_{​​​​​​2} = +8.2 C = +8.2 × 10^-6C

Also distacne from each charge d = 4.2 cm = 4.2 × 10^-2 m

Now since electric field at any point is away from positive charge and towards the negative charge, hence the resultant electric field will point towards the negative charge and electric field due to both the charges will be in same direction.

Hence, the resultant electric field at the midpoint will be given by;

Here k = 9 × 10⁹ N m^{​​​​​​2} C^{​​​​​​-2}

Substituting all the values in the above equation

Therefore, calculating from the above equation, we can get the magnitude of electric field equal to

Hence the electric field will have a magnitude of 7.5 × 10⁷ N/C in the direction of the negative charge.