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A charge q1 = +5.00 nC is placed at the origin of an xy-coordinate system, and a charge q2 = -2.00 nC is placed on the positive x-axis at x = 4.00 cm. (a) If a third charge q3 = +6.00 nC is now placed at the point x = 4.00 cm, y = 3.00 cm, find the x- and y-components of the total force exerted on this charge by the other two. (b) Find the magnitude and direction of this force.

Short Answer

Expert verified

(a) The x and y components of the total force exerted on q3are 3×105Nand respectively 6.5×105N.

(b) The magnitude of this force is 7.15×109Nand the direction is 245°from +x axis.

Step by step solution

01

Orientation of charges

The charges are aligned as given in the figure:

According to superposition principle:

Fx=F21F31cosθFy=F13sinθ

02

Components of force

x direction of force is given by

Fx=kq1q2r12+kq1q3r22×xr2=9×109×5×109×2×109(0.04)29×109×5×109×6×109×0.04(0.04)2+(0.03)23/2=3×105N

y direction of force component is given by:

Fy=kq1q3r22×yr2=9×109×5×109×6×109×0.03(0.04)2+(0.03)23/2=6.5×105N

Therefore, the x and y components of the total force exerted on q3are -3×10-5Nand 6.5×105Nrespectively.

03

Magnitude and direction of force

Magnitude of f is given by

F=Fx2+Fy2=3×1052+6.5×1052=7.15×109N

The angle is given by

α=arctan6.53=65

But is in 4th quadrant so add 180

α=65+180=245

Therefore, the magnitude of this force is 7.15×10-9Nand the direction is 245°from +x axis.

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