A point charge q is placed at origin. Let E _ A^ E _B and E _C be the electric fields at three points A(1,2,3), B(1,1,-1) and C(2,2,2) respectively due to the charge q . Then, the relation between them is 1. E _A E _B 2. E _A | E _C 3. | E _B |=4 | E _C | 4. | E _B |=8 | E _C |

Step-by-step solution

In vector form, we write expressions of field at A, B and C aligned & E _A= k q (1^2+2^2+3^2 )^ 3 / 2 ( i +2 j +3 k ) & E _B= k q (1^2+1^2+(-1)^2 )^ 3 / 2 ( i + j - k ) & E _C= k q (2^2+2^2+2^2 )^ 3 / 2 (2 i +2 j +2 k ) aligned So, aligned & E _A= k q 14^ 3 / 2 ( i +2 j +3 k ) & E _B= k q 3^ 3 / 2 ( i + j - k ) & E _C= k q 12^ 3 / 2 (2 i +2 j +2 k ) aligned As, E _A E _B=0 and E _B=4 | E _C | .