Two small insulating spheres with radius 5.50×10-2 m are separated by a large ce

Question

Two small insulating spheres with radius 5.50×10-2 m are separated by a large center-to-center distance of 0.600 m. One sphere is negatively charged, with net charge -2.50 mu C, and the other sphere is positively charged, with net charge 3.95 mu C. The charge is uniformly distributed within the volume of each sphere.
What is the magnitude E of the electric field midway between the spheres?
What is the direction of the electric field midway between the spheres?

a) toward the positively charged sphere
b) toward the negatively charged sphere
c) upward perpendicular to the line connecting the centers of the spheres
d) downward perpendicular to the line connecting the centers of the spheres

Explanation / Answer

Radius R = 0.055 m Sepration of the charges r = 0.6 m Charges q = -2.5 x 10 -6 C             q ' = 3.95 x 10 -6 C The magnitude E of the electric field midway between the spheres    E = E ' + E " Where E ' = Electric field at mid way due to q                 = Kq / r ' 2            r ' = distance of the midway from the center of one of the sphere                = r/ 2                = 0.3 m          K = Coulomb's constant              = 8.99 x 10 9 Nm 2/ C 2            r ' = distance of the midway from the center of one of the sphere                = r/ 2                = 0.3 m          K = Coulomb's constant              = 8.99 x 10 9 Nm 2/ C 2 Substitute values we get E ' = 249.722 x 10 3 N / C E " = Electric field at mid way due to q '                 = Kq' / r ' 2            r ' = distance of the midway from the center of one of the sphere                = r/ 2                = 0.3 m          K = Coulomb's constant              = 8.99 x 10 9 Nm 2/ C 2 Substitute values we get E " = 394.561 x 10 3 N / C So, E = E ' + E "          = 644.283 x 10 3 N / C                 = Kq' / r ' 2            r ' = distance of the midway from the center of one of the sphere                = r/ 2                = 0.3 m          K = Coulomb's constant              = 8.99 x 10 9 Nm 2/ C 2            r ' = distance of the midway from the center of one of the sphere                = r/ 2                = 0.3 m          K = Coulomb's constant              = 8.99 x 10 9 Nm 2/ C 2 Substitute values we get E " = 394.561 x 10 3 N / C So, E = E ' + E "          = 644.283 x 10 3 N / C

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