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an electric dipole consisting of charges of magnitude 3.10 c separated by 8.70 um is in an electric field of strength 1290 n/c. what are lal the magnitude of the electric dinole moment and lolthe ditterence betwe are (a) the magnitude of the electric dipole moment and (b) the difference between the potential energies for dipole orientations parallel and antiparallel to e?

User Yo Chauhan
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1 Answer

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Answer:

To find the magnitude of the electric dipole moment, we use the formula:

p = q * d

Where:

p is the magnitude of the electric dipole moment,

q is the charge of each charge in the electric dipole, and

d is the distance between the charges.

In your case, q = 3.10 C (Coulombs) and d = 8.70 μm (micrometers). However, we need to convert micrometers to meters before plugging the values into the formula. So, d = 8.70 × 10^(-6) m.

Now, we can calculate the magnitude of the electric dipole moment:

p = (3.10 C) * (8.70 × 10^(-6) m)

p = 2.697 × 10^(-5) C⋅m

Therefore, the magnitude of the electric dipole moment is 2.697 × 10^(-5) C⋅m.

Moving on to the difference between the potential energies for parallel and antiparallel dipole orientations. The potential energy of an electric dipole in an electric field is given by:

U = -p * E * cos(θ)

Where:

U is the potential energy,

p is the magnitude of the electric dipole moment,

E is the strength of the electric field, and

θ is the angle between the electric dipole moment and the electric field.

For parallel orientation, θ = 0°, and for antiparallel orientation, θ = 180°.

(a) The magnitude of the electric dipole moment is already calculated as 2.697 × 10^(-5) C⋅m.

(b) To find the difference between potential energies, we substitute the values into the formula:

U_parallel = -p * E * cos(0°) = -p * E

U_antiparallel = -p * E * cos(180°) = p * E

Taking the difference:

ΔU = U_parallel - U_antiparallel

ΔU = -p * E - (p * E)

ΔU = -2p * E

Substituting the values:

ΔU = -2 * (2.697 × 10^(-5) C⋅m) * (1290 N/C)

ΔU = -6.9686 × 10^(-2) J

Therefore, the difference between the potential energies for dipole orientations parallel and antiparallel to the electric field is approximately -6.9686 × 10^(-2) J, with a negative sign indicating a decrease in potential energy.

User Dean Barnes
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