(d) belotric field electric field at a distance of 1.0 m from a charged There is 100N/C At what distance from the sphere spherne electric field be 50N/C ? (7.3) T/I (a) 1.1 m (b) 1.4 m (c) 2.0 m (d) 4.0 m

The electric field strength (E) due to a point charge (or a uniformly charged sphere, which behaves like a point charge for points outside the sphere) is inversely proportional to the square of the distance (r) from the charge. This relationship is given by:<br /><br />E ∝ 1/r²<br /><br />This means that if we double the distance, the electric field strength becomes one-fourth. If we halve the distance, the electric field strength becomes four times larger.<br /><br />We can set up a proportion:<br /><br />E₁/E₂ = r₂²/r₁²<br /><br />Where:<br /><br />* E₁ is the initial electric field strength (100 N/C)<br />* r₁ is the initial distance (1.0 m)<br />* E₂ is the final electric field strength (50 N/C)<br />* r₂ is the final distance (what we want to find)<br /><br />Plugging in the values:<br /><br />100 N/C / 50 N/C = r₂² / (1.0 m)²<br /><br />2 = r₂² / 1 m²<br /><br />r₂² = 2 m²<br /><br />r₂ = √2 m ≈ 1.4 m<br /><br />So the answer is (b) 1.4 m<br />