Two short dipoles A and B, A having charges ±2 μC and length 1 cm and B having charges ±4 μC and length 1 cm, are placed with their centres 80 cm apart as shown in the figure [B is vertical at the left end with its + charge above and - below; A is horizontal at the right end, lying along the line o…

Question

Two short dipoles A and B, A having charges ±2 μC and length 1 cm and B having charges ±4 μC and length 1 cm, are placed with their centres 80 cm apart as shown in the figure [B is vertical at the left end with its + charge above and - below; A is horizontal at the right end, lying along the line of centres with its - charge nearer to P and + beyond; P is the mid-point of the 80 cm line joining the two centres]. The electric field at the point P, equidistant from the centres of both dipoles, is N C⁻¹.

Accepted Answer

(2) 9/(16)√2×10⁴. Dipole moments: p_A=2×10⁻⁶×0.01=2×10⁻⁸ and p_B=4×10⁻⁶×0.01=4×10⁻⁸ C m. P is the mid-point, so r=0.40 m from each centre and r³=0.064 m³. A lies along the line of centres, so P is on its AXIS: E_A=(2kp_A)/(r³)=(2×9×10⁹×2×10⁻⁸)/(0.064)=5625 N C⁻¹. B is perpendicular to that line, so P is on its EQUATOR: E_B=(kp_B)/(r³)=(9×10⁹×4×10⁻⁸)/(0.064)=5625 N C⁻¹. The two are mutually perpendicular, so E=√5625²+5625²=5625√2=9/(16)√2×10⁴ N C⁻¹.

Step-by-step solution

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