Let q1=5.5×10−9C, q2=4×10−9C, r=100mm=0.1m. The electric field produced by the first sphere at some distance x from it is given as follows:
E1=kx2q1 where k is the constant and x is the distance from the center of the first sphere. The second sphere produces the following field at the same point x:
E2=k(r−x)2q2 These fields are directed in opposite direction, thus, the resulting field is zero if
E1=E2 Solving for x, obtain:
kx2q1=k(r−x)2q2q1(r−x)2=q2x2q1r2−2q1rx+q1x2=q2x2(q1−q2)x2−2q1rx+q1r2=01.5×10−9x2−1.1×10−9x+0.055×10−9=01.5x2−1.1x+0.055=0x1≈0.054m=5.4cmx2≈0.68m=68cm Answer. The electric magnetic field magnitude is zero at 5.4cm and 68 cm from the first particle.
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