Question

2. (r>>d) (a) A dipole with charges ±q and separation d is placed on the y axis as shown in the right figure (?p = q?d). Express the Electric field at the point A to the simplest form with the given constants(d,p,?,r). You may use (1 + x)? ? 1 + nx, (x ? 1). Also, you can use both cartesian coordinate or polar coordinate. [+6 pt] (b) Another dipole with same charges and separation is placed on the point A. The new dipole forms an angle of ?' with the x axis. Express the torque and potential energy of the dipole with the given letter. [4 pt]

          2.
(r>>d)
(a) A dipole with charges ±q and separation d is placed on the y axis as shown in the right figure (?p = q?d). Express the Electric field at the point A to the simplest form with the given constants(d,p,?,r). You may use (1 + x)? ? 1 + nx, (x ? 1). Also, you can use both cartesian coordinate or polar coordinate. [+6 pt]
(b) Another dipole with same charges and separation is placed on the point A. The new dipole forms an angle of ?' with the x axis. Express the torque and potential energy of the dipole with the given letter. [4 pt]

2.
(r>>d)
(a) A dipole with charges ±q and separation d is placed on the y axis as shown in the right figure (?p = q?d). Express the Electric field at the point A to the simplest form with the given constants(d,p,?,r). You may use (1 + x)? ? 1 + nx, (x ? 1). Also, you can use both cartesian coordinate or polar coordinate. [+6 pt]
(b) Another dipole with same charges and separation is placed on the point A. The new dipole forms an angle of ?' with the x axis. Express the torque and potential energy of the dipole with the given letter. [4 pt]

Added by Mohamed M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

08/30/2023

Step 1

The electric field due to the positive charge at A is: $$E_+ = \frac{kq}{r_+^2}$$ where $r_+$ is the distance from the positive charge to point A, which is $\frac{d}{2}$. Similarly, the electric field due to the negative charge at A is: $$E_- = Show more…

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(a) A dipole with charges ±q and separation d is placed on the y axis as shown in the right figure (p₀ = qd₀). Express the Electric field at the point A to the simplest form with the given constants(d,p,Θ,r). You may use (1 + x)ⁿ ≅ 1 + nx, (x ≪ 1). Also, you can use both cartesian coordinate or polar coordinate. (b) Another dipole with same charges and separation is placed on the point A. The new dipole forms an angle of θ' with the x axis. Express the torque and potential energy of the dipole with the given letter.