The electric potential in a region of space is V = a + bx 3 , where a = 300.0 V

Question

The electric potential in a region of space is V = a + bx 3 , where a = 300.0 V and b = - 0.0 0 2 V/m 3 . The initial acceleration of an electron ( m = 9.1 1 x 10 - 31 kg, q = - 1.6 0 x 10 - 19 C) placed at x = 0.7 0 m is A. 9.81 x 10 15 m/s 2 along the positive x – axis. B. 7.33 x 10 13 m/s 2 along the negative x – axis. C. 2.64 x 10 11 m/s 2 along the positive x – axis. D. 5.16 x 10 8 m/s 2 a long the negative x – axis. E. 1.12 x 10 5 m/s 2 along the positive x – axis.

14. The electric potential in a region of space is V-a + bx, where a = 300.0 V and b =-0.002 Vm3. The initial acceleration of an electron (m-9.11 x 10-31 kg, q--1.60 x 10-19 C) placed at x = 0.70 m is A. 9.81 x 1015 m/s along the positive x-axis. B. 7.33 x 1013 m/s' along the negative x-axis. 1.60 x 101placed at x C. 2.64 x 10 m/s along the positive x-axs D. 5.16 x 10s m/s2 along the negative x-axis. E. 1.12x 10*m/s along the positive x-axis. 11 2 E. 1.12x 10*m/s? along the positive x-axis.

Explanation / Answer

Electric field, E = -dV/dx = -3bx2

At x = 0.70 m, E = -3 * (-0.002) * 0.702 = 2.94 * 10-3 N/C

Acceleration of the electron, a = qE/m = (-1.6 * 10-19) * (2.94 * 10-3) / (9.11 * 10-31) = -5.16 * 108 m/s

Negative sign indicates acceleration is towards the negative x-axis.

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