Figure 1. Two charges +q and  −q are separated by a distance  2a with  +q lying at  x=−a and  −q at  x=a. Point  P sits at 

Sunday, 26 August 2018

12:46 AM

Machine generated alternative text: Question: O x=-a •p Figure 1. Two charges -eq and —q are separated by a distance 2awith -eq lyingat = —a and —q at x = a. Point P sits at > a. A dipole consists of opposite and equal charges A-q and —q, separated by a distance 2a. Point P is a distance x from the centre of this dipole along the axis drawn through the üo charges as shown in the figure (witn +q atx = —a and —q atr = a). Take the potential an infinite distance from a point charge to be 0, (V = 0). Give your expressions in terms of eo, not Coulomb's constant part 1) Write an expression tor the potential at P due to just the A-q charge. part 2) Write an expression tor the total potential at P due to this dipole. Simplify your expression (but do not make the approximation a x). part 3) using this expression derive an expression tor the electric field in the direction in the region x > a. Check

 

Machine generated alternative text: Feedback tor Part 1) The potential a distance d from a point charge q is given by: qx —qa—qx— qa -2 In this case, q = q and d + a so: 47rE0 d 47rE0 x4-a • Marks for this submissiom 0.00/0.33. This submission attracted a penalty of 0.11 Feedback tor Part 2) Potentials obey the Éw of superposition so we can add these potentials Marks for this submissiom 0.00/0.33. This submission attracted a penalty of 0.11 Feedback tor Part 3) The electric field is related to the potential difference through: In this case Marks for this submissiom 0.00/0.33. This submission attracted a penalty of 0.11 47rE0 47rE0 1 1 d x4-a x 4-a 47rE0 47rE0 2 — 02 ) 27rE0 (x 2 —a 27rE0 27rE0 — ) -d-(x2 —a2) I (2x) x (x2 —2xqa 2 a

 

Machine generated alternative text: A correct answer is which can be typed in as follows: •(z4a) q/ (4 (x+a)) A correct answer — •(x2 —a2) A correct answer — - (a (%pi , which can be typed in as follows: -aA2)) , which can be typed in as follows: -aA2)A2)

 

 

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