A point charge +6q is located at the origin, and a point charge -4q is located on the x-axis at D = 0.530 m. At what location on the x-axis will a third charge, q0, experience no net force from the other two charges?

Explanation:

A point charge (+6q) at the origin I.e at (0,0)

Another point(-4q) charge is located at (0.53m, 0)

Both charges are on the x axis

Where will a third charge be place and it will experience no net force?

Fnet=0 due to charge 3

The location of qo should be at positive x axis, beyond q2(-4q), so has to have a stable charges.

Let the distance of -4q from qo be x

Then from +6q to qo is 0.56+x

The third charge has a charge of q.

Now we need to find Fnet due to charge 3.

Fnet= F13+F23

Let find F13

Let the distance of q1 from charge qo is 0.56+x

Both q1 and q3 are positive, there will be a force of repulsion between them, the F13 will be in the direction of positive x axis

F13=kq1q3/r²

q1= +6q and q3=q

F13=k6qq/(0.56+x)²

F13=k6q²/(0.56+x)²

In vector form

F13=k6q²/(0.56+x)² i

Now let find F23

q2 is negative and q3 is positive, a force or attraction will occur between the two bodies, then the F23 will move in the negative direction of x-axis

Given that, q2=(-4q) and q3=q, r=x

F23=kq1q3/r²

q1= +6q and q3=q

F23=k4qq/x²

F23=k4q²/x²

In vector form

F23=—k4q²/x² i

So, Fnet=F23+F13

Fnet= —k4q²/x²i + k6q²/(0.56+x)² i

Since Fnet=0

Then,

O=—k4q²/x² + k6q²/(0.56+x)²

k4q²/x² = k6q²/(0.56+x)²

Divide through by k2q², then we have

2/x²=3/(0.56+x)²

2(0.56+x)²=3x²

2(0.3136+1.12x+x²)=3x²

0.6272+2.24x+2x²=3x²

3x²-2x²-0.6272-2.24x=0

x²—2.24x—0.6272=0

Using formula method

a =1 b=-2.24 and x=-0.6272

x=-b±sqrt(b²-4ac)/2a

x=2.24±sqrt(-2.24²-4×1×-0.6272)/2×1

x=2.24±sqrt(5.0176+2.5088)/2

x=2.24±sqrt(7.5264)/2

x=(2.24±2.74)/2

Then x=(2.24+2.74)/2

x=2.49

or x=(2.24-2.74)/2

x=-0.25

So, x will be at (0.53+x) from the origin

1. When x =2.49

(0.53+2.49)=3.02m

2. When x =-0.25

This will not be possible because it will be attracted by the charges.

x=-0.25+0.53

x=0.28m

electromagnetic shielding is the practice of reducing the electromagnetic field in a space by blocking the field with barriers made of conductive or magnetic materials. shielding is typically applied to enclosures to isolate electrical devices from their surroundings, and to cables to isolate wires from the environment through which the cable runs. electromagnetic shielding that blocks radio frequency electromagnetic radiation is also known as rf shielding.

the shielding can reduce the coupling of radio waves, electromagnetic fields and electrostatic fields. a conductive enclosure used to block electrostatic fields is also known as a faraday cage. the amount of reduction depends very much upon the material used, its thickness, the size of the shielded volume and the frequency of the fields of interest and the size, shape and orientation of apertures in a shield to an incident electromagnetic

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