Elect+theory

# Elect+theory - 1 A thundercloud has the charge distribution...

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1. A thundercloud has the charge distribution as shown on the diagram. Treat this distribution as two point charges, a negative charge of -30 C at the height of 2 km above the ground and a positive charge of +30 C at the height of 3 km . The presence of these charges induces charges on the ground. Assuming the ground is a conductor, it can be shown that the induced charges can be treated as a charge of +30 C at the depth of 2 km below ground level and a charge of -30 C at the depth of 3 km . Consider point P 1 , which is just above the ground directly below the thundercloud, and point P 2 , which is 1 km horizontally away from P 1 . a) Determine direction and magnitude of electric field at these points. b) Letting zero of potential to be at infinity, determine the potential at these points 2. A rod of uniform linear charge density +1.5 x 10 -5 C / m is bent into an arc of radius R = 0.10 m . The arc is placed with its center at the origin of the axis. A proton is placed at point O and held at rest. a) Determine the magnitude and direction of the force required to keep the proton at rest. (Ignore the effects of gravity) b) Determine the electric potential at point O . 3. A spherical cloud of radius R contains total charge +Q with a nonuniform volume charge density that varies according to the equation ) 1 ( ) ( 0 R r r - = ρ for R r

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and 0 = ρ for R r , where r is the distance from the center of the cloud. Determine electric field E and electric potential U as a function of r . If proton is placed in point P and released, what is it going to move like after a long time after its release? 4. A loop of wire of width w and height h contains a switch and a battery and is connected to a spring of force constant k . The loop carries a current I in a clockwise direction, and its bottom is in constant, uniform magnetic field directed into the plane of the page. a) If the switch is opened, the loop eventually comes to rest at a new equilibrium position that is a distance x from its former position. Derive an expression for the magnitude B of the uniform magnetic field in terms of given quantities and
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Elect+theory - 1 A thundercloud has the charge distribution...

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