In an otherwise empty region of space, two small objects with equal magnitudes of net charge are located 1 meter apart. 1. Sketch the electric field around these two objects if they have the same sign of charge. Make a separate drawing showing equipotential lines around the two charges. The potential is defined to be zero at infinity. Identify the line of zero potential between the two charges, if there is one. 2. Now assume that the two charges have opposite signs. Sketch the electric field around these two objects. Make a separate drawing showing equipotential lines around the two charges. The potential is defined to be zero at infinity. Identify the line of zero potential between the two charges, if there is one. 3. For each of the two possibilities (the same or opposite sign of charge) is the total work done to bring the charges together positive or negative?
In an otherwise empty region of space, two small objects with equal magnitudes of net charge are located 1 meter apart.
1. Sketch the electric field around these two objects if they have the same sign of charge. Make a separate drawing showing equipotential lines around the two charges. The potential is defined to be zero at infinity. Identify the line of zero potential between the two charges, if there is one.
2. Now assume that the two charges have opposite signs. Sketch the electric field around these two objects. Make a separate drawing showing equipotential lines around the two charges. The potential is defined to be zero at infinity. Identify the line of zero potential between the two charges, if there is one.
3. For each of the two possibilities (the same or opposite sign of charge) is the total work done to bring the charges together positive or negative?
Useful equations:
Potential energy: U(r)=kqQr,ΔU=qΔV
Potential difference: ΔVAB=VB−VA=−∫ABE→⋅dl→=−Wq(A→B)q
Electric potential: V=kqr=k∫dqr
The electric field from potential: E→=−∇→V=−i^∂V∂x−j^∂V∂y−k^∂V∂z=−r^∂V∂r−θ^1r∂V∂θ−ϕ^1rsinθ∂V∂ϕfor planar and spherical coordinates, respectively.
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